Oscillations

A particle of mass m oscillates with simple harmonic motion between points x1 and x2, the equilibrium position being O. Its potential energy is plotted. It will be as given below in the graph

1. [figure]
2. [figure]
3. [figure]
4. [figure]

The time period of mass suspended from a spring is T. If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be

1. T/4
2. T
3. T/2
4. 2T

In case of a forced vibration, the resonance peak becomes very sharp when the

1. damping force is small
2. restoring force is small
3. applied periodic force is small
4. quality factor is small

Displacement between maximum potential energy position and maximum kinetic energy position for a particle executing simple harmonic motion is

1. a/2
2. +a
3. a
4. -1

When an oscillator completes 100 oscillations its amplitude is reduced to 13 of initial value. What will be its amplitude, when it completes 200 oscillations?

1. 18
2. 23
3. 16
4. 19

A mass is suspended separately by two different springs in successive order, then time periods are t1 and t2 respectively. If it is connected by both springs as shown in figure then time period is t0, the correct relation is [figure]

1. t02 = t12 + t22
2. t0-2 = t1-2 + t2-2
3. t0-1 = t1-1 + t2-1
4. t0 = t1 + t2

The total energy of particle performing SHM depends on

1. k, a, m
2. k, a
3. k, a, x
4. k, x

Two masses MA and MB are hung from two strings of length lA and lB respectively. They are executing SHM with frequency relation fA = 2fB, then relation

1. lA = lB4, does not depend on mass
2. lA = 4lB, does not depend on mass
3. lA = 2lB and MA = 2MB
4. lA = lB2 and MA = MB2

The bob of simple pendulum having length l, is displaced from mean position to an angular position with respect to vertical. If it is released, then velocity of bob at equilibrium position

1. 2gl(1 - )
2. 2gl(1 + )
3. 2gl
4. 2gl

The equations of two waves acting in perpendicular directions are given as x = a ( t + ) and y = a ( t + ), where = + 2, the resultant wave represents

1. a parabola
2. a circle
3. an ellipse
4. a straight line