### 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
• 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