Oscillations

A particle of mass m oscillates along x-axis according to equation x = a t. The nature of the graph between momentum and displacement of the particle is

1. Circle
2. Hyperbola
3. Ellipse
4. Straight line passing through origin

Two particles are oscillating along two close parallel straight lines side by side, with the same frequency and amplitudes. They pass each other, moving in opposite directions when their displacement is half of the amplitude. The mean positions of the two particles lie on a straight line perpendicular to the paths of the two particles. The phase difference is

1. 6
2. 0
3. 2 3

A particle of mass m is released from rest and follows a parabolic path as shown. Assuming that the displacement of the mass from the origin is small, which graph correctly depicts the position of the particle as a function of time? [figure]

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

Out of the following functions representing motion of a particle which represents SHM (1) y = sin t - cos t (2) y = sin3 t (3) y = 5 cos ( 3 4 - 3 t ) (4) y = 1 + t + 2 t2

1. Only (1)
2. Only (4) does not represent SHM
3. Only (1) and (3)
4. Only (1) and (2)

The displacement of a particle along the x-axis is given by x = a 2 . The motion of the particle corresponds to

1. simple harmonic motion of frequency /
2. simple harmonic motion of frequency 3 /2
3. non simple harmonic motion
4. simple harmonic motion of frequency /2

The period of oscillation of a mass M suspended from a spring of negligible mass is T. If along with it another mass M is also suspended, the period of oscillation will now be

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

A simple pendulum performs simple harmonic motion about x = 0 with an amplitude a and time period T. The speed of the pendulum at x = a/2 will be

1. aT
2. 3 2 aT
3. a 3T
4. a 32T

Which one of the following equations of motion represents simple harmonic motion ? where k, k0, k1 and a are all positive.

1. Acceleration = -k(x + a)
2. Acceleration = k(x + a)
3. Acceleration = - 2x
4. Acceleration = -k0x + k1x2

Two simple harmonic motions of angular frequency 100 and 1000 rad s-1 have the same displacement amplitude. The ratio of their maximum acceleration is

1. 1 : 103
2. 1 : 104
3. 1 : 10
4. 1 : 102

A point performs simple harmonic oscillation of period T and the equation of motion is given by x = a ( t + /6). After the elapse of what fraction of the time period the velocity of the point will be equal to half of its maximum velocity?

1. T/3
2. T/12
3. T/8
4. T/6