Oscillations Physics - Oscillations

The rotation of earth about its axis is:

1. Periodic motion.
2. Simple harmonic motion.
3. Periodic but not simple harmonic motion.
4. Non-periodic motion.

A particle is in linear simple harmonic motion between two points A and B, 10cm apart Take the direction from A to B as the + ve direction and choose the correct statements:

1. The sign of velocity, acceleration and force on the particle when it is 3cm away from A going towards B are positive.
2. The sign of velocity of the particle at C going towards O is negative.
3. The sign of velocity, acceleration and force on the particle when it is 4cm away from B going towards A are negative.
4. The sign of acceleration and force on the particle when it is at point B is negative.

Four pendulums A, B, C and D are suspended from the same elastic support as shown in Fig A and C are of the same length, while B is smaller than A and D is larger than A. If A is given a transverse displacement,

1. D will vibrate with maximum amplitude.
2. C will vibrate with maximum amplitude.
3. B will vibrate with maximum amplitude.
4. All the four will oscillate with equal amplitude.

Motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lower point is:

1. Simple harmonic motion.
2. Non-periodic motion.
3. Periodic motion.
4. Periodic but not S.H.M.

Motion of an oscillating liquid column in a U-tube is:

1. Periodic but not simple harmonic.
2. Non-periodic.
3. Simple harmonic and time period is independent of the density of the liquid.
4. Simple harmonic and time-period is directly proportional to the density of the liquid.

A mass of 2kg is attached to the spring of spring constant 50Nm^–1 . The block is pulled to a distance of 5cm from its equilibrium position at x = 0 on a horizontal frictionless surface from rest at t = 0. Write the expression for its displacement at anytime t.

Two identical springs of spring constant K are attached to a block of mass m and to fixed supports as shown in Fig. When the mass is displaced from equilllibrium position by a distance x towards right, find the restoring force.

Consider a pair of identical pendulums, which oscillate with equal amplitude independently such that when one pendulum is at its extreme position making an angle of 2° to the right with the vertical, the other pendulum makes an angle of 1° to the left of the vertical. What is the phase difference between the pendulums?

What are the two basic characteristics of a simple harmonic motion?

Displacement versus time curve for a particle executing S.H.M. is shown in Fig. Identify the points marked at which,

1. Velocity of the oscillator is zero,
2. Speed of the oscillator is maximum.

Find the displacement of a simple harmonic oscillator at which its PE is half of the maximum energy of the oscillator.

What is the ratio of maxmimum acceleration to the maximum velocity of a simple harmonic oscillator?

When will the motion of a simple pendulum be simple harmonic?

One end of a V-tube containing mercury is connected to a suction pump and the other end to atmosphere. The two arms of the tube are inclined to horizontal at an angle of 45 PHA° each. A small pressure difference is created between two columns when the suction pump is removed. Will the column of mercury in V-tube execute simple harmonic motion? Neglect capillary and viscous forces.Find the time period of oscillation.

Draw a graph to show the variation of P.E., K.E. and total energy of a simple harmonic oscillator with displacement.

The length of a second’s pendulum on the surface of Earth is 1m. What will be the length of a second’s pendulum on the moon?