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qUESTIONS

The period of oscillation of a body of mass m₁ suspended from a light spring is T. When a body of mass m, is tied to the first body and the system is made to oscillate, the period is 27. Compare the masses m₁ and m₂

Find the change in length of a second’s pendulum, if the acceleration due to gravity at the place changes from 9.75 m/s² to 9.8 m/s².

A simple pendulum of length 100 cm performs S.H.M. Find the restoring force acting on its bob of mass 50 g when the displacement from the mean position is 3 cm.

A simple pendulum performs S.H.M of period 4 seconds. How much time after crossing the mean position, will the displacement of the bob be one third of its amplitude.

Two magnets with the same dimensions and mass, but of magnetic moments mu_{1} = 100A * m² and mu_{2} = 50A * m² are jointly suspended in the earth’s magnetic field so as to perform angular oscillations in a horizontal plane. When their like poles are joined together, the period of their angular S.H.M. is 5 s. Find the period of angular S.H.M. when their unlike poles are joined together.

A bar magnet of mass 120 g, in the form of a rectangular paralleleπped, has dimensions l = 40mm b = 10 mm and h = 80 mm. With the dimension h vertical, the magnet performs angular oscillations in the plane of a magnetic field with period π . If its magnetic moment is 3.4 A m² , determine the influencing magnetic field.

The period of oscillations of a simple pendulum increases by 10%, when its length is increased by 21cm. Find its initial length and initial period.

In summer season, a pendulum clock is regulated as a second’s pendulum and it keeps correct time. During winter, the length of the pendulum decreases by 1%. How much will the clock gain or lose in one day.

The displacement of an oscillating particle is given by x = asinωt + bcosωt where a, b and ω are constants. Prove that the particle performs a linear S.H.M. with amplitude A = √ (a² + b²)

A particle performing linear S.H.M. of period 2π seconds about the mean position O is observed to have a speed of b √ 3 m/s, when at a distance b (metre) from O. If the particle is moving away from O at that instant, find the time required by the particle, to travel a further distance b.

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