Oscillations Questions and Answers Part-7

1.A particle of mass 10 gm is describing S.H.M. along a straight line with period of 2 sec and amplitude of 10 cm. Its kinetic energy when it is at 5 cm from its equilibrium position is
a) \[37.5\pi^{2}ergs\]
b) \[3.75\pi^{2}ergs\]
c) \[375\pi^{2}ergs\]
d) \[0.375\pi^{2}ergs\]

Answer: c
Explanation:
q61

2. When the displacement is half the amplitude, the ratio of potential energy to the total energy is
a) \[\frac{1}{2}\]
b) \[\frac{1}{4}\]
c) 1
d) \[\frac{1}{8}\]

Answer: b
Explanation:
q62

3. The P.E. of a particle executing SHM at a distance x from its equilibrium position is
a) \[\frac{1}{2}m\omega^{2}x ^{2}\]
b) \[\frac{1}{2}m\omega^{2}a ^{2}\]
c) \[\frac{1}{2}m\omega^{2}\left(a ^{2}-x ^{2}\right)\]
d) Zero

Answer: a
Explanation: \[\frac{1}{2}m\omega^{2}X ^{2}\]

4. A vertical mass-spring system executes simple harmonic oscillations with a period of 2 s. A quantity of this system which exhibits simple harmonic variation with a period of 1 s is
a) Velocity
b) Potential energy
c) Phase difference between acceleration and displacement
d) Difference between kinetic energy and potential energy

Answer: a
Explanation: The time period of potential energy and kinetic energy is half that of SHM.

5. For any S.H.M., amplitude is 6 cm. If instantaneous potential energy is half the total energy then distance of particle from its mean position is
a) 3 cm
b) 4.2 cm
c) 5.8 cm
d) 6 cm

Answer: b
Explanation:
q65

6. A body of mass kg 1 is executing simple harmonic motion. Its displacement y(cm) at t seconds is given by \[y=6\sin\left(100t+ \pi/4\right)\]    . Its maximum kinetic energy is
a) 6 J
b) 18 J
c) 24 J
d) 36 J

Answer: b
Explanation:
q66

7. A particle is executing simple harmonic motion with frequency f. The frequency at which its kinetic energy change into potential energy is
a) \[f/2\]
b) f
c) 2 f
d) 4 f

Answer: c
Explanation: In S.H.M., frequency of K.E. and P.E. = 2 * (Frequency of oscillating particle)

8. There is a body having mass m and performing S.H.M. with amplitude a. There is a restoring force \[F=-kx\]   , where x is the displacement. The total energy of body depends upon
a) K, x
b) K, a
c) K, a, x
d) K, a, v

Answer: b
Explanation:
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9. The total energy of a particle executing S.H.M. is 80 J. What is the potential energy when the particle is at a distance of 3/4 of amplitude from the mean position
a) 60 J
b) 10 J
c) 40 J
d) 45 J

Answer: d
Explanation:
q69

10. In a simple harmonic oscillator, at the mean position
a) Kinetic energy is minimum, potential energy is maximum
b) Both kinetic and potential energies are maximum
c) Kinetic energy is maximum, potential energy is minimum
d) Both kinetic and potential energies are minimum

Answer: c
Explanation: Kinetic energy is maximum, potential energy is minimum