DC Pandey Solutions (JEE Advance): Simple Harmonic Motion | DC Pandey Solutions for JEE Physics PDF Download

 Page 1


For JEE Advanced 
  Assertion and Reason 
  Directions : Choose the correct option. 
  (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion. 
  (b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion. 
  (c) If Assertion is true, but the Reason is false. 
  (d) If Assertion is false but the Reason is true. 
Q 1.  Assertion : In x = A cos ?t, x is the displacement measured from extreme position.  
  Reason : In the above equation x = A at time t = 0. 
Q 2.  Assertion : A particle is under SHM along the x-axis. Its mean position is x = 2, amplitude is A = 
2 and angular frequency ?. At t = 0, particle is at origin, then x-co-ordinate versus time equation 
of the particle will be x = - 2 cos ?t + 2. 
  Reason : At t = 0, particle is at rest. 
Q 3.  Assertion : A spring block system is kept over a smooth surface as shown in figure. If a constant 
horizontal force F is applied on the
 
block it will start oscillating simple harmonically. 
 
  Reason : Time period of oscillation is less than 
m
2
k
? . 
Q 4.  Assertion : Time taken by a particle in SHM to move from x = A to x = 
3A
2
is same as the time 
taken by the particle to move from 
3A A
x to x
22
?? . 
  Reason : Corresponding angles rotated in the reference circle are same in the given time intervals. 
Q 5.  Assertion : Path of a particle in SHM is always a straight line.  
  Reason : All straight line motions are not simple harmonic. 
Q 6.  Assertion : In spring block system if length of spring and mass of block both are halved, then 
angular frequency of oscillations will remain unchanged. 
  Reason : Angular frequency is given by 
k
m
?? 
Q 7.  Assertion : All small oscillations are simple harmonic in nature. 
Reason : Oscillations of spring block system are always simple harmonic whether amplitude is 
small or large. 
Q 8.  Assertion : In x = A cos ?t, the dot product of acceleration and velocity is positive for time 
interval 0< t < 
2
?
?
. 
  Reason : Angle between them is 0°. 
Page 2


For JEE Advanced 
  Assertion and Reason 
  Directions : Choose the correct option. 
  (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion. 
  (b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion. 
  (c) If Assertion is true, but the Reason is false. 
  (d) If Assertion is false but the Reason is true. 
Q 1.  Assertion : In x = A cos ?t, x is the displacement measured from extreme position.  
  Reason : In the above equation x = A at time t = 0. 
Q 2.  Assertion : A particle is under SHM along the x-axis. Its mean position is x = 2, amplitude is A = 
2 and angular frequency ?. At t = 0, particle is at origin, then x-co-ordinate versus time equation 
of the particle will be x = - 2 cos ?t + 2. 
  Reason : At t = 0, particle is at rest. 
Q 3.  Assertion : A spring block system is kept over a smooth surface as shown in figure. If a constant 
horizontal force F is applied on the
 
block it will start oscillating simple harmonically. 
 
  Reason : Time period of oscillation is less than 
m
2
k
? . 
Q 4.  Assertion : Time taken by a particle in SHM to move from x = A to x = 
3A
2
is same as the time 
taken by the particle to move from 
3A A
x to x
22
?? . 
  Reason : Corresponding angles rotated in the reference circle are same in the given time intervals. 
Q 5.  Assertion : Path of a particle in SHM is always a straight line.  
  Reason : All straight line motions are not simple harmonic. 
Q 6.  Assertion : In spring block system if length of spring and mass of block both are halved, then 
angular frequency of oscillations will remain unchanged. 
  Reason : Angular frequency is given by 
k
m
?? 
Q 7.  Assertion : All small oscillations are simple harmonic in nature. 
Reason : Oscillations of spring block system are always simple harmonic whether amplitude is 
small or large. 
Q 8.  Assertion : In x = A cos ?t, the dot product of acceleration and velocity is positive for time 
interval 0< t < 
2
?
?
. 
  Reason : Angle between them is 0°. 
Q 9.  Assertion : In simple harmonic motion displacement and acceleration always have a constant ratio. 
 Reason : 
displacement
T2
acceleration
?? 
Q 10.  Assertion : We can call circular motion also as simple harmonic motion. 
Reason : Angular velocity in uniform circular motion and angular frequency in simple harmonic 
motion have the same meanings. 
Answers 
1. (d) 2. (b) 3. (c) 4. (a) 5. (d) 6. (d) 7. (d) 8. (a) 9. (a) 10. (d) 
 
Solutions 
1.  For, x = A cos at, particle is at x = A at 
  t = 0, but the displacement is measured from mean position. So, assertion is false. 
2.  Assertion and reason are both true but reason is not correct explanation. 
3.  Assertion is true while time period of oscillation is  so, the reason is false.  
4.  
   
   
   
   
  Reason correctly explains assertion. 
5.  In uniform circular motion also particle performs SHM, so assertion is false. 
6.  If spring is halved, then spring constant becomes twice and as mass is halved, then  
  i.e., angular frequency gets double. Thus, assertion is false. 
7.  Assertion is false as if then motion will not be SHM. 
8.  For x = A cos ?t between t = 0 to 
2
?
?
, particle moves from one extreme to mean position such 
that velocity and acceleration are in same direction, i.e., angle between them is zero. Such that 
Page 3


For JEE Advanced 
  Assertion and Reason 
  Directions : Choose the correct option. 
  (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion. 
  (b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion. 
  (c) If Assertion is true, but the Reason is false. 
  (d) If Assertion is false but the Reason is true. 
Q 1.  Assertion : In x = A cos ?t, x is the displacement measured from extreme position.  
  Reason : In the above equation x = A at time t = 0. 
Q 2.  Assertion : A particle is under SHM along the x-axis. Its mean position is x = 2, amplitude is A = 
2 and angular frequency ?. At t = 0, particle is at origin, then x-co-ordinate versus time equation 
of the particle will be x = - 2 cos ?t + 2. 
  Reason : At t = 0, particle is at rest. 
Q 3.  Assertion : A spring block system is kept over a smooth surface as shown in figure. If a constant 
horizontal force F is applied on the
 
block it will start oscillating simple harmonically. 
 
  Reason : Time period of oscillation is less than 
m
2
k
? . 
Q 4.  Assertion : Time taken by a particle in SHM to move from x = A to x = 
3A
2
is same as the time 
taken by the particle to move from 
3A A
x to x
22
?? . 
  Reason : Corresponding angles rotated in the reference circle are same in the given time intervals. 
Q 5.  Assertion : Path of a particle in SHM is always a straight line.  
  Reason : All straight line motions are not simple harmonic. 
Q 6.  Assertion : In spring block system if length of spring and mass of block both are halved, then 
angular frequency of oscillations will remain unchanged. 
  Reason : Angular frequency is given by 
k
m
?? 
Q 7.  Assertion : All small oscillations are simple harmonic in nature. 
Reason : Oscillations of spring block system are always simple harmonic whether amplitude is 
small or large. 
Q 8.  Assertion : In x = A cos ?t, the dot product of acceleration and velocity is positive for time 
interval 0< t < 
2
?
?
. 
  Reason : Angle between them is 0°. 
Q 9.  Assertion : In simple harmonic motion displacement and acceleration always have a constant ratio. 
 Reason : 
displacement
T2
acceleration
?? 
Q 10.  Assertion : We can call circular motion also as simple harmonic motion. 
Reason : Angular velocity in uniform circular motion and angular frequency in simple harmonic 
motion have the same meanings. 
Answers 
1. (d) 2. (b) 3. (c) 4. (a) 5. (d) 6. (d) 7. (d) 8. (a) 9. (a) 10. (d) 
 
Solutions 
1.  For, x = A cos at, particle is at x = A at 
  t = 0, but the displacement is measured from mean position. So, assertion is false. 
2.  Assertion and reason are both true but reason is not correct explanation. 
3.  Assertion is true while time period of oscillation is  so, the reason is false.  
4.  
   
   
   
   
  Reason correctly explains assertion. 
5.  In uniform circular motion also particle performs SHM, so assertion is false. 
6.  If spring is halved, then spring constant becomes twice and as mass is halved, then  
  i.e., angular frequency gets double. Thus, assertion is false. 
7.  Assertion is false as if then motion will not be SHM. 
8.  For x = A cos ?t between t = 0 to 
2
?
?
, particle moves from one extreme to mean position such 
that velocity and acceleration are in same direction, i.e., angle between them is zero. Such that 
  
as
 
then = positive. Thus, reason is true explanation of assertion. 
9.  In SHM, a = - ?
2
x,  
   
  So, reason is correct explanation of assertion. 
10.  Only uniform circular motion can be called SHM, so, assertion is false. 
 
Objective Questions Single Correct Option 
Q 1.  A particle of mass 2 kg moves in simple harmonic motion and its potential energy U varies with 
position x as shown. The period of oscillation of the particle
 
is 
 
 (a) 
2
s
5
?
   (b) 
22
s
5
?
   (c) 
2
s
5
?
   (d) 
4
s
5
?
  
Q 2.  In the figure shown, a spring mass system is placed on a horizontal smooth surface in between two 
vertical rigid walls W 1 and W 2. One end of spring is fixed with wall W 1 and other end is attached 
with mass m which is free to move. Initially, spring is tension free and having natural length l 0. 
Mass m is compressed through a distance a and released. Taking the collision between wall W 2 
and mass m as elastic and K as spring constant, the average force exerted by mass m on wall W 2 in 
one oscillation of block is 
 
 (a) 
2aK
?
  (b) 
2ma
?
   (c) 
aK
?
   (d) 
2aK
m
 
Q 3.  Two simple harmonic motions are represented by the following equations y = 40 sin ?t
 
and  
y2 = 10(sin ?t + c cos ?t).
 
If their displacement amplitudes are equal, then the value of c (in 
appropriate units) is 
(a) 13   (b) 15   (c) 17   (d) 4 
Q 4.  A particle executes simple harmonic motion with frequency 2.5 Hz and amplitude 2 m. The speed 
of the particle 0.3 s after crossing, the equilibrium position is 
(a) zero  (b) 2 ? m/s  (c) 4 ? m/s  (d) ? m/s 
Page 4


For JEE Advanced 
  Assertion and Reason 
  Directions : Choose the correct option. 
  (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion. 
  (b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion. 
  (c) If Assertion is true, but the Reason is false. 
  (d) If Assertion is false but the Reason is true. 
Q 1.  Assertion : In x = A cos ?t, x is the displacement measured from extreme position.  
  Reason : In the above equation x = A at time t = 0. 
Q 2.  Assertion : A particle is under SHM along the x-axis. Its mean position is x = 2, amplitude is A = 
2 and angular frequency ?. At t = 0, particle is at origin, then x-co-ordinate versus time equation 
of the particle will be x = - 2 cos ?t + 2. 
  Reason : At t = 0, particle is at rest. 
Q 3.  Assertion : A spring block system is kept over a smooth surface as shown in figure. If a constant 
horizontal force F is applied on the
 
block it will start oscillating simple harmonically. 
 
  Reason : Time period of oscillation is less than 
m
2
k
? . 
Q 4.  Assertion : Time taken by a particle in SHM to move from x = A to x = 
3A
2
is same as the time 
taken by the particle to move from 
3A A
x to x
22
?? . 
  Reason : Corresponding angles rotated in the reference circle are same in the given time intervals. 
Q 5.  Assertion : Path of a particle in SHM is always a straight line.  
  Reason : All straight line motions are not simple harmonic. 
Q 6.  Assertion : In spring block system if length of spring and mass of block both are halved, then 
angular frequency of oscillations will remain unchanged. 
  Reason : Angular frequency is given by 
k
m
?? 
Q 7.  Assertion : All small oscillations are simple harmonic in nature. 
Reason : Oscillations of spring block system are always simple harmonic whether amplitude is 
small or large. 
Q 8.  Assertion : In x = A cos ?t, the dot product of acceleration and velocity is positive for time 
interval 0< t < 
2
?
?
. 
  Reason : Angle between them is 0°. 
Q 9.  Assertion : In simple harmonic motion displacement and acceleration always have a constant ratio. 
 Reason : 
displacement
T2
acceleration
?? 
Q 10.  Assertion : We can call circular motion also as simple harmonic motion. 
Reason : Angular velocity in uniform circular motion and angular frequency in simple harmonic 
motion have the same meanings. 
Answers 
1. (d) 2. (b) 3. (c) 4. (a) 5. (d) 6. (d) 7. (d) 8. (a) 9. (a) 10. (d) 
 
Solutions 
1.  For, x = A cos at, particle is at x = A at 
  t = 0, but the displacement is measured from mean position. So, assertion is false. 
2.  Assertion and reason are both true but reason is not correct explanation. 
3.  Assertion is true while time period of oscillation is  so, the reason is false.  
4.  
   
   
   
   
  Reason correctly explains assertion. 
5.  In uniform circular motion also particle performs SHM, so assertion is false. 
6.  If spring is halved, then spring constant becomes twice and as mass is halved, then  
  i.e., angular frequency gets double. Thus, assertion is false. 
7.  Assertion is false as if then motion will not be SHM. 
8.  For x = A cos ?t between t = 0 to 
2
?
?
, particle moves from one extreme to mean position such 
that velocity and acceleration are in same direction, i.e., angle between them is zero. Such that 
  
as
 
then = positive. Thus, reason is true explanation of assertion. 
9.  In SHM, a = - ?
2
x,  
   
  So, reason is correct explanation of assertion. 
10.  Only uniform circular motion can be called SHM, so, assertion is false. 
 
Objective Questions Single Correct Option 
Q 1.  A particle of mass 2 kg moves in simple harmonic motion and its potential energy U varies with 
position x as shown. The period of oscillation of the particle
 
is 
 
 (a) 
2
s
5
?
   (b) 
22
s
5
?
   (c) 
2
s
5
?
   (d) 
4
s
5
?
  
Q 2.  In the figure shown, a spring mass system is placed on a horizontal smooth surface in between two 
vertical rigid walls W 1 and W 2. One end of spring is fixed with wall W 1 and other end is attached 
with mass m which is free to move. Initially, spring is tension free and having natural length l 0. 
Mass m is compressed through a distance a and released. Taking the collision between wall W 2 
and mass m as elastic and K as spring constant, the average force exerted by mass m on wall W 2 in 
one oscillation of block is 
 
 (a) 
2aK
?
  (b) 
2ma
?
   (c) 
aK
?
   (d) 
2aK
m
 
Q 3.  Two simple harmonic motions are represented by the following equations y = 40 sin ?t
 
and  
y2 = 10(sin ?t + c cos ?t).
 
If their displacement amplitudes are equal, then the value of c (in 
appropriate units) is 
(a) 13   (b) 15   (c) 17   (d) 4 
Q 4.  A particle executes simple harmonic motion with frequency 2.5 Hz and amplitude 2 m. The speed 
of the particle 0.3 s after crossing, the equilibrium position is 
(a) zero  (b) 2 ? m/s  (c) 4 ? m/s  (d) ? m/s 
Q 5.  A particle oscillates simple harmonically with a period of 16 s. Two second after crossing the 
equilibrium position its velocity becomes 1 m/s. The amplitude is 
 (a) m
4
?
   (b) 
82
m
?
   (c) 
8
m
?
   (d) 
42
m
?
 
Q 6.  A seconds pendulum is suspended from the ceiling of a trolley moving horizontally with an 
acceleration of 4 m/s
2
. Its period of oscillation is 
  (a) 1.90 s   (b) 1.70 s  (c) 2.30 s   (d) 1.40 s 
Q 7.  A particle is performing a linear simple harmonic motion. If the instantaneous acceleration and 
velocity of the particle are a and v respectively, identify the graph which correctly represents the 
relation between a and v 
  (a)  (b) (c)  (d) 
Q 8.  In a vertical U-tube a column of mercury oscillates simple harmonically. If the tube contains 1 kg 
of mercury and 1 cm of mercury column weighs 20 g, then the period of oscillation is 
  (a) 1s    (b) 2 s   (c) 2s   (d) Insufficient data 
Q 9.  A solid cube of side a and density ?0
 
floats on the surface of a liquid of density ?.
 
If the cube is 
slightly
 
pushed downward, then it oscillates simple harmonically with a period of 
 (a) 
0
a
2
g
?
?
?
   (b) 
0
a
2
g
?
?
?
   (c) 
0
a
2
1g
?
?? ?
?
??
?
??
 (d) 
0
a
2
1g
?
?? ?
?
??
?
??
 
Q 10.  A particle of mass m is attached with three springs A, B and C of equal force constants k as shown 
in figure. The particle is pushed slightly against the spring C
 
and released, the time period of 
oscillation will be 
 
 (a) 
m
2
k
?   (b) 
m
2
2k
?   (c) 
m
2
3k
?   (d) 
m
2
5k
? 
Q 11.  A uniform stick of length l is mounted so as to rotate about a horizontal axis perpendicular to the 
stick and at a distance d from the centre of mass. The time period of small oscillations has a 
minimum value when d/l is 
 (a) 
1
2
   (b) 
1
12
   (c) 
1
3
   (d) 
1
6
 
Q 12.  Three arrangements of spring-mass system are shown in figures (A), (B) and (C). If T1, T2 and T3 
represent the respective periods of oscillation, then correct relation is 
Page 5


For JEE Advanced 
  Assertion and Reason 
  Directions : Choose the correct option. 
  (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion. 
  (b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion. 
  (c) If Assertion is true, but the Reason is false. 
  (d) If Assertion is false but the Reason is true. 
Q 1.  Assertion : In x = A cos ?t, x is the displacement measured from extreme position.  
  Reason : In the above equation x = A at time t = 0. 
Q 2.  Assertion : A particle is under SHM along the x-axis. Its mean position is x = 2, amplitude is A = 
2 and angular frequency ?. At t = 0, particle is at origin, then x-co-ordinate versus time equation 
of the particle will be x = - 2 cos ?t + 2. 
  Reason : At t = 0, particle is at rest. 
Q 3.  Assertion : A spring block system is kept over a smooth surface as shown in figure. If a constant 
horizontal force F is applied on the
 
block it will start oscillating simple harmonically. 
 
  Reason : Time period of oscillation is less than 
m
2
k
? . 
Q 4.  Assertion : Time taken by a particle in SHM to move from x = A to x = 
3A
2
is same as the time 
taken by the particle to move from 
3A A
x to x
22
?? . 
  Reason : Corresponding angles rotated in the reference circle are same in the given time intervals. 
Q 5.  Assertion : Path of a particle in SHM is always a straight line.  
  Reason : All straight line motions are not simple harmonic. 
Q 6.  Assertion : In spring block system if length of spring and mass of block both are halved, then 
angular frequency of oscillations will remain unchanged. 
  Reason : Angular frequency is given by 
k
m
?? 
Q 7.  Assertion : All small oscillations are simple harmonic in nature. 
Reason : Oscillations of spring block system are always simple harmonic whether amplitude is 
small or large. 
Q 8.  Assertion : In x = A cos ?t, the dot product of acceleration and velocity is positive for time 
interval 0< t < 
2
?
?
. 
  Reason : Angle between them is 0°. 
Q 9.  Assertion : In simple harmonic motion displacement and acceleration always have a constant ratio. 
 Reason : 
displacement
T2
acceleration
?? 
Q 10.  Assertion : We can call circular motion also as simple harmonic motion. 
Reason : Angular velocity in uniform circular motion and angular frequency in simple harmonic 
motion have the same meanings. 
Answers 
1. (d) 2. (b) 3. (c) 4. (a) 5. (d) 6. (d) 7. (d) 8. (a) 9. (a) 10. (d) 
 
Solutions 
1.  For, x = A cos at, particle is at x = A at 
  t = 0, but the displacement is measured from mean position. So, assertion is false. 
2.  Assertion and reason are both true but reason is not correct explanation. 
3.  Assertion is true while time period of oscillation is  so, the reason is false.  
4.  
   
   
   
   
  Reason correctly explains assertion. 
5.  In uniform circular motion also particle performs SHM, so assertion is false. 
6.  If spring is halved, then spring constant becomes twice and as mass is halved, then  
  i.e., angular frequency gets double. Thus, assertion is false. 
7.  Assertion is false as if then motion will not be SHM. 
8.  For x = A cos ?t between t = 0 to 
2
?
?
, particle moves from one extreme to mean position such 
that velocity and acceleration are in same direction, i.e., angle between them is zero. Such that 
  
as
 
then = positive. Thus, reason is true explanation of assertion. 
9.  In SHM, a = - ?
2
x,  
   
  So, reason is correct explanation of assertion. 
10.  Only uniform circular motion can be called SHM, so, assertion is false. 
 
Objective Questions Single Correct Option 
Q 1.  A particle of mass 2 kg moves in simple harmonic motion and its potential energy U varies with 
position x as shown. The period of oscillation of the particle
 
is 
 
 (a) 
2
s
5
?
   (b) 
22
s
5
?
   (c) 
2
s
5
?
   (d) 
4
s
5
?
  
Q 2.  In the figure shown, a spring mass system is placed on a horizontal smooth surface in between two 
vertical rigid walls W 1 and W 2. One end of spring is fixed with wall W 1 and other end is attached 
with mass m which is free to move. Initially, spring is tension free and having natural length l 0. 
Mass m is compressed through a distance a and released. Taking the collision between wall W 2 
and mass m as elastic and K as spring constant, the average force exerted by mass m on wall W 2 in 
one oscillation of block is 
 
 (a) 
2aK
?
  (b) 
2ma
?
   (c) 
aK
?
   (d) 
2aK
m
 
Q 3.  Two simple harmonic motions are represented by the following equations y = 40 sin ?t
 
and  
y2 = 10(sin ?t + c cos ?t).
 
If their displacement amplitudes are equal, then the value of c (in 
appropriate units) is 
(a) 13   (b) 15   (c) 17   (d) 4 
Q 4.  A particle executes simple harmonic motion with frequency 2.5 Hz and amplitude 2 m. The speed 
of the particle 0.3 s after crossing, the equilibrium position is 
(a) zero  (b) 2 ? m/s  (c) 4 ? m/s  (d) ? m/s 
Q 5.  A particle oscillates simple harmonically with a period of 16 s. Two second after crossing the 
equilibrium position its velocity becomes 1 m/s. The amplitude is 
 (a) m
4
?
   (b) 
82
m
?
   (c) 
8
m
?
   (d) 
42
m
?
 
Q 6.  A seconds pendulum is suspended from the ceiling of a trolley moving horizontally with an 
acceleration of 4 m/s
2
. Its period of oscillation is 
  (a) 1.90 s   (b) 1.70 s  (c) 2.30 s   (d) 1.40 s 
Q 7.  A particle is performing a linear simple harmonic motion. If the instantaneous acceleration and 
velocity of the particle are a and v respectively, identify the graph which correctly represents the 
relation between a and v 
  (a)  (b) (c)  (d) 
Q 8.  In a vertical U-tube a column of mercury oscillates simple harmonically. If the tube contains 1 kg 
of mercury and 1 cm of mercury column weighs 20 g, then the period of oscillation is 
  (a) 1s    (b) 2 s   (c) 2s   (d) Insufficient data 
Q 9.  A solid cube of side a and density ?0
 
floats on the surface of a liquid of density ?.
 
If the cube is 
slightly
 
pushed downward, then it oscillates simple harmonically with a period of 
 (a) 
0
a
2
g
?
?
?
   (b) 
0
a
2
g
?
?
?
   (c) 
0
a
2
1g
?
?? ?
?
??
?
??
 (d) 
0
a
2
1g
?
?? ?
?
??
?
??
 
Q 10.  A particle of mass m is attached with three springs A, B and C of equal force constants k as shown 
in figure. The particle is pushed slightly against the spring C
 
and released, the time period of 
oscillation will be 
 
 (a) 
m
2
k
?   (b) 
m
2
2k
?   (c) 
m
2
3k
?   (d) 
m
2
5k
? 
Q 11.  A uniform stick of length l is mounted so as to rotate about a horizontal axis perpendicular to the 
stick and at a distance d from the centre of mass. The time period of small oscillations has a 
minimum value when d/l is 
 (a) 
1
2
   (b) 
1
12
   (c) 
1
3
   (d) 
1
6
 
Q 12.  Three arrangements of spring-mass system are shown in figures (A), (B) and (C). If T1, T2 and T3 
represent the respective periods of oscillation, then correct relation is 
 
  (a) T1 > T2 > T3  (b) T3 > T2 > T, (c) T2 > T1 > T3  (d) T2 > T3 > T1 
Q 13.  Three arrangements are shown in figure. 
 
  (A) A spring of mass m and stiffness k 
  (B) A block of mass m attached to massless spring of stiffness k 
  (C) A block of mass 
m
2
attached to a spring of mass 
m
2
and stiffness k 
If T1 T2 and T3 represent the period of oscillation in the three cases respectively, then identify the 
correct relation 
  (a) T1<T2<T3   (b) T1<T3<T2   (c) T1>T3>T2   (d) T3 <T1<T2 
Q 14.  A block of mass M is kept on a smooth surface and touches the two springs as shown in the figure 
but not attached to the springs. Initially springs are in their natural length. Now, the block is 
shifted (l 0/2) from the given position in such a way that it compresses a spring and released. The 
time-period of oscillation of mass will be 
 
 (a) 
M
2k
?
   (b) 
M
2
5k
?  (c) 
3M
2k
?
   (d) 
M
2k
?  
Q 15.  A particle moving on x-axis has potential energy U = 2 - 20x + 5x
2
 Joule along x-axis. The 
particle is released at x = - 3. The maximum value of x will be (x is in metre) 
  (a) 5 m   (b) 3 m   (c) 7 m   (d) 8 m 
Q 16.  A block of mass m, when attached to a uniform ideal spring with force constant k and free length 
L executes SHM. The spring is then cut in two pieces, one with free length n L and other with free 
length (1 - n) L. The block is also divided in the same fraction. The smaller part of the block 
attached to longer part of the spring executes SHM with frequency f1. The bigger part of the block 
attached
 
to smaller part of the spring executes SHM with frequency f 2. The ratio f 1/ f 2 is