Oscillations

A rectangular block of mass m and area of cross-section A floats in a liquid of density . If it is given a small vertical displacement from equilibrium it undergoes oscillation with a time period T, then

1. T 1 m
2. T
3. T 1 A
4. T 1

The circular motion of a particle with constant speed is

1. periodic but not simple harmonic
2. simple harmonic but not periodic
3. periodic and simple harmonic
4. neither periodic nor simple harmonic

A particle executing simple harmonic motion of amplitude 5 cm has maximum speed of 31.4 cm/s. The frequency of its oscillation is

1. 4 Hz
2. 3 Hz
3. 2 Hz
4. 1 Hz

Two springs of spring constants k1 and k2 are joined in series. The effective spring constant of the combination is given by

1. k1k2
2. (k1 + k2)/2
3. k1 + k2
4. k1k2/(k1 + k2)

Which one of the following statements is true for the speed v and the acceleration a of a particle executing simple harmonic motion?

1. When v is maximum, a is maximum
2. Value of a is zero, whatever may be the value of v.
3. When v is zero, a is zero
4. When v is maximum, a is zero.

The potential energy of a simple harmonic oscillator when the particle is half way to its end point is

1. 23E
2. 18E
3. 14E
4. 12E

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