Q 1. A body is executing simple harmonic motion with frequency 'n', the frequency of its potential energy is: [2021]
A: 3n
B: 4n
C: n
D: 2n
Ans: D
Solution: Displacement equation of SHM of frequency 'n' x = Asin(ωt) = Asin(2πnt) Now,
So frequency of potential energy = 2n
Q 2. A spring is stretched by 5 cm by a force 10 N. The time period of the oscillations when a mass of 2 kg is suspended by it is: [2021]
A: 3.14 s
B: 0.628 s
C: 0.0628 s
D: 6.28 s
Ans:
Solution:
F = kx
10 = k(5 × 10^{–2})
= 2 x 10^{2}
= 200 N/m
Now,
3. Average velocity of a particle executing SHM in one complete vibration is: [2019]
A: Aω/2
B: Aω
C:
D: Zero
Ans: D
Solution:
In one complete vibration, displacement is zero. So, average velocity in one complete vibration
Q 4. The displacement of a particle executing simple harmonic motion is given by y = A_{0}+ Asinωt + Bcosωt
Then the amplitude of its oscillation is given by : [2019]
A:
B:
C:
D: A + B
Ans: B
Solution:
y = A_{0}+ Asinωt + Bsinωt
Equate SHM
y' = y – A_{0} = Asinωt + Bcosωt
Resultant amplitude
Q 5. The radius of circle, the period of revolution, initial position and sense of revolution are indicated in the fig.
y  projection of the radius vector of rotating particle P is: [2019]
A: y(t) = –3 cos2πt, where y in m
B:
C:
D:
Ans: D
Solution:
At t = 0, y displacement is maximum, so equation will be cosine function.
T = 4s
y = a cosωt
Q 6. A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is 20 m/s^{2} at a distance of 5 m from the mean position. The time period of oscillation is: [2018]
A: 2πs
B: πs
C: 2s
D: 1s
Ans: B
Solution:
Q 7. A particle executes linear simple harmonic motion with an amplitude of 3 cm. When the particle is at 2 cm from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is: [2017]
A:
B:
C:
D:
Ans: B
Solution:
Q 8. A particle is executing SHM along a straight line. Its velocities at distances x_{1} and x_{2} from the mean position are V_{1} and V_{2}, respectively. Its time period is: [2015]
A:
B:
C:
D:
Ans: C
Solution:
Q 9. When two displacements represented by y_{1} = a sin(ωt) and y_{2} = b cos(ωt) are superimposed the motion is: [2015]
A: simple harmonic with amplitude (a+b)/2
B: not a simple harmonic
C: simple harmonic with amplitude a/b
D: simple harmonic with amplitude
Ans: D
Solution:
where c^{2} = a^{2} + b^{2 }[since a^{2 }+ b^{2} = c^{2} cos (φ) + c^{2 }sin (φ) = c^{2}^{ }]
The superimposed motion is simple harmonic with amplitude
Q 10. The oscillation of a body on a smooth horizontal surface is represented by the equation,
X = A cos (ωt)
Where X = displacement at time t
ω = frequency of oscillation
Which one of the following graphs shows correctly the variation ‘a’ with ‘t’? [2014]
A:
B:
C:
D:
Here, a = acceleration at time ‘t’ and T = time period
Ans: A
Solution:
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