Physics - Oscillations

Question - 1

In the case of simple pendulum, executing simple harmonic motion, the force supplying centripetal acceleration is

  • A \(mgcos\theta \)
  • B \(mgsin\theta \)
  • C \(-mgcos\theta \)
  • D \(-mgsin\theta \)

Question - 2

In the spring-mass system, if the mass of the system is doubled with spring constant halved, the natural frequency of longitudinal vibration

  • A is doubled
  • B is quadrupled
  • C is halved
  • D remains same

Question - 3

If the spring-mass system is a very high altitude, the natural frequency of longitudinal vibration

  • A decreases
  • B increases
  • C becomes infinite
  • D remains unchanged

Question - 4

The following equation represents the displacement y (in m) of a particle executing simple harmonic motion as a function of time t 

\(y=0.6sin(4\pi t+0.5\pi )cos(4\pi t+0.5\pi )\) It has frequency,initial phase and amplitude respectively as

  • A 4 Hz,0.5 rad and 0.6 m
  • B 4 Hz,\(\pi \) rad and 0.3 m
  • C 8 Hz, 0.5 rad and 0.3 m
  • D 8 Hz,\(\pi \) rad and 0.6 m

Question - 5

In simple harmonic motion, when the displacement is one-half the amplitude, what fraction of total energy is potential energy?

  • A 0.25
  • B 0.50
  • C 0.75
  • D 0.67

Question - 6

In the spring-mass system, the frequency of oscillation does not depend on

  • A the magnitude of displacement
  • B the magnitude of mass suspended
  • C the mass of the spring
  • D the magnitude of displacement and the mass of the spring

Question - 7

A mass M is attached to a spring whose upper end is fixed. The mass and stiffness k of the spring are m and k respectively. The natural frequency of the spring-mass system is

  • A \(\nu =\frac { 1 }{ 2\pi } \sqrt { \frac { k }{ M+m } } \)
  • B \(r=\frac { 1 }{ 2\pi } \sqrt { \frac { k }{ M } } \)
  • C \(\nu =\frac { 1 }{ 2\pi } \sqrt { \frac { 3k }{ 3M+m } } \)
  • D \(r=\frac { 1 }{ 2\pi } \sqrt { \frac { 3k }{ M+3m } } \)

Question - 8

For a simple pendulum in motion, if the effect of air resistance is taken into account, which parameter is constant of motion

  • A Energy
  • B Angluar momentum
  • C Restoring force
  • D Frequency of vibration

Question - 9

In a spring-mass system, of mass m and stiffness k, the ends of the spring are securely fixed and mass is attached to intermediate point of spring. The natural frequency of longitudinal vibration of the system.

  • A is minimum when the mass is attached to the mid-point of the spring
  • B is maximum when the mass is attached to the mid-point of the spring
  • C decreases as the distance from the bottom end whose mass is attached,decreases
  • D decreases as the distance from the top and where mass is attached, decreases

Question - 10

A light spring AC of stiffness 2k is cut at B into two halves AB and BC. The point A is connected to a upper rigid support whereas point C is connected to a lower rigid support. The common point B is connected to a certain mass m. The new system will vibrate with frequency, as compared to spring AC with the same mass m,

  • A \(\sqrt { 2 } \) times the previous value
  • B 2 times the previous value
  • C 4 times the previous value
  • D 2\(\sqrt { 2 } \) times the previous value
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