SHM and oscillations: JEE Mains Previous Year Questions (2021-2024) | Physics for JEE Main & Advanced PDF Download

 Page 1


Previous Year Questions (2021-24): 
Simple Harmonic Motion (Oscillations) 
2024 
Q1 - 2024 (01 Feb Shift 2) 
A mass ?? is suspended from a spring of negligible mass and the system oscillates with 
a frequency ?? 1
. The frequency of oscillations if a mass 9 m is suspended from the same 
spring is f
2
. The value of 
f
1
f
2
 is 
Q2 - 2024 (27 Jan Shift 1) 
A particle executes simple harmonic motion with an amplitude of 4 cm. At the mean 
position, velocity of the particle is 10 cm / s. The distance of the particle from the mean 
position when its speed becomes 5 cm / s is v ?? cm, where ?? = 
Q3 - 2024 (27 Jan Shift 2) 
A ball suspended by a thread swings in a vertical plane so that its magnitude of 
acceleration in the extreme position and lowest position are equal. The angle ( ?? ) of 
thread deflection in the extreme position will be : 
(1) ta n
- 1
? ( v 2 ) 
(2) 2 ta n
- 1
? (
1
2
) 
(3) ta n
- 1
? (
1
2
) 
(4) 2 ta n
- 1
? (
1
v 5
) 
Q4 - 2024 (29 Jan Shift 1) 
When the displacement of a simple harmonic oscillator is one third of its amplitude, the 
ratio of total energy to the kinetic energy is 
?? 8
, where x = 
Q5 - 2024 (29 Jan Shift 2) 
A simple harmonic oscillator has an amplitude A and time period 6 ?? second. Assuming 
the oscillation starts from its mean position, the time required by it to travel from ?? = ?? 
to ?? =
v 3
2
?? will be 
?? x
s, where x = 
Page 2


Previous Year Questions (2021-24): 
Simple Harmonic Motion (Oscillations) 
2024 
Q1 - 2024 (01 Feb Shift 2) 
A mass ?? is suspended from a spring of negligible mass and the system oscillates with 
a frequency ?? 1
. The frequency of oscillations if a mass 9 m is suspended from the same 
spring is f
2
. The value of 
f
1
f
2
 is 
Q2 - 2024 (27 Jan Shift 1) 
A particle executes simple harmonic motion with an amplitude of 4 cm. At the mean 
position, velocity of the particle is 10 cm / s. The distance of the particle from the mean 
position when its speed becomes 5 cm / s is v ?? cm, where ?? = 
Q3 - 2024 (27 Jan Shift 2) 
A ball suspended by a thread swings in a vertical plane so that its magnitude of 
acceleration in the extreme position and lowest position are equal. The angle ( ?? ) of 
thread deflection in the extreme position will be : 
(1) ta n
- 1
? ( v 2 ) 
(2) 2 ta n
- 1
? (
1
2
) 
(3) ta n
- 1
? (
1
2
) 
(4) 2 ta n
- 1
? (
1
v 5
) 
Q4 - 2024 (29 Jan Shift 1) 
When the displacement of a simple harmonic oscillator is one third of its amplitude, the 
ratio of total energy to the kinetic energy is 
?? 8
, where x = 
Q5 - 2024 (29 Jan Shift 2) 
A simple harmonic oscillator has an amplitude A and time period 6 ?? second. Assuming 
the oscillation starts from its mean position, the time required by it to travel from ?? = ?? 
to ?? =
v 3
2
?? will be 
?? x
s, where x = 
Questions with Answer Keys 
A simple pendulum is placed at a place where its distance from the earth's surface is 
equal to the radius of the earth. If the length of the string is 4 m, then the time period of 
small oscillations will be s. [ take g = ?? 2
 ms
- 2
] 
Q7 - 2024 (31 Jan Shift 1) 
A particle performs simple harmonic motion with amplitude A. Its speed is increased to 
three times at an instant when its displacement is 
2 A
3
. The new amplitude of motion is 
nA
3
. The value of n is 
Q8 - 2024 (31 Jan Shift 2) 
The time period of simple harmonic motion of mass ?? in the given figure is ?? v
????
5 ?? , 
where the value of ?? is 
 
 
Answer Key 
Q1 (3) 
Q2 (12) 
Q3 (2) 
Q4 (9) 
Q5 (2) 
Q6 (8) 
Q7 (7) 
Q8 (12) 
 
Page 3


Previous Year Questions (2021-24): 
Simple Harmonic Motion (Oscillations) 
2024 
Q1 - 2024 (01 Feb Shift 2) 
A mass ?? is suspended from a spring of negligible mass and the system oscillates with 
a frequency ?? 1
. The frequency of oscillations if a mass 9 m is suspended from the same 
spring is f
2
. The value of 
f
1
f
2
 is 
Q2 - 2024 (27 Jan Shift 1) 
A particle executes simple harmonic motion with an amplitude of 4 cm. At the mean 
position, velocity of the particle is 10 cm / s. The distance of the particle from the mean 
position when its speed becomes 5 cm / s is v ?? cm, where ?? = 
Q3 - 2024 (27 Jan Shift 2) 
A ball suspended by a thread swings in a vertical plane so that its magnitude of 
acceleration in the extreme position and lowest position are equal. The angle ( ?? ) of 
thread deflection in the extreme position will be : 
(1) ta n
- 1
? ( v 2 ) 
(2) 2 ta n
- 1
? (
1
2
) 
(3) ta n
- 1
? (
1
2
) 
(4) 2 ta n
- 1
? (
1
v 5
) 
Q4 - 2024 (29 Jan Shift 1) 
When the displacement of a simple harmonic oscillator is one third of its amplitude, the 
ratio of total energy to the kinetic energy is 
?? 8
, where x = 
Q5 - 2024 (29 Jan Shift 2) 
A simple harmonic oscillator has an amplitude A and time period 6 ?? second. Assuming 
the oscillation starts from its mean position, the time required by it to travel from ?? = ?? 
to ?? =
v 3
2
?? will be 
?? x
s, where x = 
Questions with Answer Keys 
A simple pendulum is placed at a place where its distance from the earth's surface is 
equal to the radius of the earth. If the length of the string is 4 m, then the time period of 
small oscillations will be s. [ take g = ?? 2
 ms
- 2
] 
Q7 - 2024 (31 Jan Shift 1) 
A particle performs simple harmonic motion with amplitude A. Its speed is increased to 
three times at an instant when its displacement is 
2 A
3
. The new amplitude of motion is 
nA
3
. The value of n is 
Q8 - 2024 (31 Jan Shift 2) 
The time period of simple harmonic motion of mass ?? in the given figure is ?? v
????
5 ?? , 
where the value of ?? is 
 
 
Answer Key 
Q1 (3) 
Q2 (12) 
Q3 (2) 
Q4 (9) 
Q5 (2) 
Q6 (8) 
Q7 (7) 
Q8 (12) 
 
Solutions 
Q1 
f
1
=
1
2 ?? v
k
m
 
f
2
=
1
2 ?? v
k
9 m
 
f
1
f
2
=
v
9
1
=
3
1
 
Q2 
V
ut mean position 
= A ?? ? 10 = 4 ?? 
?? =
5
2
 
v = ?? v A
2
- x
2
 
5 =
5
2
v 4
2
- x
2
? x
2
= 16 - 4 
x = v 12 cm 
Q3 
 
Loss in kinetic energy = Gain in potential energy 
Page 4


Previous Year Questions (2021-24): 
Simple Harmonic Motion (Oscillations) 
2024 
Q1 - 2024 (01 Feb Shift 2) 
A mass ?? is suspended from a spring of negligible mass and the system oscillates with 
a frequency ?? 1
. The frequency of oscillations if a mass 9 m is suspended from the same 
spring is f
2
. The value of 
f
1
f
2
 is 
Q2 - 2024 (27 Jan Shift 1) 
A particle executes simple harmonic motion with an amplitude of 4 cm. At the mean 
position, velocity of the particle is 10 cm / s. The distance of the particle from the mean 
position when its speed becomes 5 cm / s is v ?? cm, where ?? = 
Q3 - 2024 (27 Jan Shift 2) 
A ball suspended by a thread swings in a vertical plane so that its magnitude of 
acceleration in the extreme position and lowest position are equal. The angle ( ?? ) of 
thread deflection in the extreme position will be : 
(1) ta n
- 1
? ( v 2 ) 
(2) 2 ta n
- 1
? (
1
2
) 
(3) ta n
- 1
? (
1
2
) 
(4) 2 ta n
- 1
? (
1
v 5
) 
Q4 - 2024 (29 Jan Shift 1) 
When the displacement of a simple harmonic oscillator is one third of its amplitude, the 
ratio of total energy to the kinetic energy is 
?? 8
, where x = 
Q5 - 2024 (29 Jan Shift 2) 
A simple harmonic oscillator has an amplitude A and time period 6 ?? second. Assuming 
the oscillation starts from its mean position, the time required by it to travel from ?? = ?? 
to ?? =
v 3
2
?? will be 
?? x
s, where x = 
Questions with Answer Keys 
A simple pendulum is placed at a place where its distance from the earth's surface is 
equal to the radius of the earth. If the length of the string is 4 m, then the time period of 
small oscillations will be s. [ take g = ?? 2
 ms
- 2
] 
Q7 - 2024 (31 Jan Shift 1) 
A particle performs simple harmonic motion with amplitude A. Its speed is increased to 
three times at an instant when its displacement is 
2 A
3
. The new amplitude of motion is 
nA
3
. The value of n is 
Q8 - 2024 (31 Jan Shift 2) 
The time period of simple harmonic motion of mass ?? in the given figure is ?? v
????
5 ?? , 
where the value of ?? is 
 
 
Answer Key 
Q1 (3) 
Q2 (12) 
Q3 (2) 
Q4 (9) 
Q5 (2) 
Q6 (8) 
Q7 (7) 
Q8 (12) 
 
Solutions 
Q1 
f
1
=
1
2 ?? v
k
m
 
f
2
=
1
2 ?? v
k
9 m
 
f
1
f
2
=
v
9
1
=
3
1
 
Q2 
V
ut mean position 
= A ?? ? 10 = 4 ?? 
?? =
5
2
 
v = ?? v A
2
- x
2
 
5 =
5
2
v 4
2
- x
2
? x
2
= 16 - 4 
x = v 12 cm 
Q3 
 
Loss in kinetic energy = Gain in potential energy 
?
1
2
mv
2
= mg l ( 1 - co s ? ?? ) 
?
v
2
l
= 2 g ( 1 - co s ? ?? ) 
Acceleration at lowest point =
v
2
l
 
Acceleration at extreme point = ?? s in ? ?? 
Hence, 
?? 2
l
= g s in ? ?? 
? s in ? ?? = 2 ( 1 - co s ? ?? ) 
? ta n ?
?? 2
=
1
2
? ?? = 2 ta n
- 1
? (
1
2
) 
Q4 
Let total energy = E =
1
2
KA
2
 
U =
1
2
 K (
A
3
)
2
=
KA
2
2 × 9
=
E
9
 
KE = E -
E
9
=
8E
9
 
Ratio 
 Total 
KE
=
E
8E
9
=
9
8
 
x = 9 
Q5 
 
From phasor diagram particle has to move from P to Q in a circle of radius equal to 
amplitude of S H M. 
Page 5


Previous Year Questions (2021-24): 
Simple Harmonic Motion (Oscillations) 
2024 
Q1 - 2024 (01 Feb Shift 2) 
A mass ?? is suspended from a spring of negligible mass and the system oscillates with 
a frequency ?? 1
. The frequency of oscillations if a mass 9 m is suspended from the same 
spring is f
2
. The value of 
f
1
f
2
 is 
Q2 - 2024 (27 Jan Shift 1) 
A particle executes simple harmonic motion with an amplitude of 4 cm. At the mean 
position, velocity of the particle is 10 cm / s. The distance of the particle from the mean 
position when its speed becomes 5 cm / s is v ?? cm, where ?? = 
Q3 - 2024 (27 Jan Shift 2) 
A ball suspended by a thread swings in a vertical plane so that its magnitude of 
acceleration in the extreme position and lowest position are equal. The angle ( ?? ) of 
thread deflection in the extreme position will be : 
(1) ta n
- 1
? ( v 2 ) 
(2) 2 ta n
- 1
? (
1
2
) 
(3) ta n
- 1
? (
1
2
) 
(4) 2 ta n
- 1
? (
1
v 5
) 
Q4 - 2024 (29 Jan Shift 1) 
When the displacement of a simple harmonic oscillator is one third of its amplitude, the 
ratio of total energy to the kinetic energy is 
?? 8
, where x = 
Q5 - 2024 (29 Jan Shift 2) 
A simple harmonic oscillator has an amplitude A and time period 6 ?? second. Assuming 
the oscillation starts from its mean position, the time required by it to travel from ?? = ?? 
to ?? =
v 3
2
?? will be 
?? x
s, where x = 
Questions with Answer Keys 
A simple pendulum is placed at a place where its distance from the earth's surface is 
equal to the radius of the earth. If the length of the string is 4 m, then the time period of 
small oscillations will be s. [ take g = ?? 2
 ms
- 2
] 
Q7 - 2024 (31 Jan Shift 1) 
A particle performs simple harmonic motion with amplitude A. Its speed is increased to 
three times at an instant when its displacement is 
2 A
3
. The new amplitude of motion is 
nA
3
. The value of n is 
Q8 - 2024 (31 Jan Shift 2) 
The time period of simple harmonic motion of mass ?? in the given figure is ?? v
????
5 ?? , 
where the value of ?? is 
 
 
Answer Key 
Q1 (3) 
Q2 (12) 
Q3 (2) 
Q4 (9) 
Q5 (2) 
Q6 (8) 
Q7 (7) 
Q8 (12) 
 
Solutions 
Q1 
f
1
=
1
2 ?? v
k
m
 
f
2
=
1
2 ?? v
k
9 m
 
f
1
f
2
=
v
9
1
=
3
1
 
Q2 
V
ut mean position 
= A ?? ? 10 = 4 ?? 
?? =
5
2
 
v = ?? v A
2
- x
2
 
5 =
5
2
v 4
2
- x
2
? x
2
= 16 - 4 
x = v 12 cm 
Q3 
 
Loss in kinetic energy = Gain in potential energy 
?
1
2
mv
2
= mg l ( 1 - co s ? ?? ) 
?
v
2
l
= 2 g ( 1 - co s ? ?? ) 
Acceleration at lowest point =
v
2
l
 
Acceleration at extreme point = ?? s in ? ?? 
Hence, 
?? 2
l
= g s in ? ?? 
? s in ? ?? = 2 ( 1 - co s ? ?? ) 
? ta n ?
?? 2
=
1
2
? ?? = 2 ta n
- 1
? (
1
2
) 
Q4 
Let total energy = E =
1
2
KA
2
 
U =
1
2
 K (
A
3
)
2
=
KA
2
2 × 9
=
E
9
 
KE = E -
E
9
=
8E
9
 
Ratio 
 Total 
KE
=
E
8E
9
=
9
8
 
x = 9 
Q5 
 
From phasor diagram particle has to move from P to Q in a circle of radius equal to 
amplitude of S H M. 
co s ? ?? =
v 3 A
2
 A
=
v 3
2
 
?? =
?? 6
 
Now, 
?? 6
= ?? t 
?? 6
=
2 ?? ?? ?? 
?? 6
=
2 ?? 6 ?? ?? 
t =
?? 2
 
So, ?? = 2 
Q6 
Acceleration due to gravity g
'
=
?? 4
 
T = 2 ?? v
4 l
g
 
T = 2 ?? v
4 × 4
 g
 
T = 2 ?? 4
?? = 8 s 
Q7 
v = ?? v A
2
- x
2
 
at x =
2 A
3
 
?? = ?? v
?? 2
- (
2 ?? 3
)
2
=
v 5 A ?? 3
 
New amplitude = ?? '