Oscillations

A mass of 2.0 kg is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible. When pressed slightly and released the mass executes a simple harmonic motion. The spring constant is 200 N/m. What should be the minimum amplitude of the motion so that the mass gets detached from the pan (take g = 10 m/s2). [figure]

1. 10.0 cm
2. any value less than 12.0 cm
3. 4.0 cm
4. 8.0 cm

The particle executing simple harmonic motion has a kinetic energy K0 2 t. The maximum values of the potential energy and the total energy are respectively

1. K0/2 and K0
2. K0 and 2K0
3. K0 and K0
4. 0 and 2K0

The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is

2. 0.707
3. zero
4. 0.5

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]