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qUESTIONS

A wooden block of mass m is kept on a piston that can perform vertical vibrations of adjustable frequency and amplitude. During vibrations, we don’t want the block to leave the contact with the πston. How much maximum frequency is possible if the amplitude of vibrations is restricted to 25 cm? In this case, how much is the energy per unit mass of the block? (g ≈ π² ≈ 10 m s²)

Find the number of oscillations performed per minute by a magnet is vibrating in the plane of a uniform field of 1.6 × 10-5 Wb/m². The magnet has moment of inertia 3 * 10² – 6 * kg / (m² ) and magnetic moment 3A * m² .

A 20 cm wide thin circular disc of mass 200 g is suspended to a rigid support from a thin metallic string. By holding the rim of the disc, the string is twisted through 60º and released. It now performs angular oscillations of period 1 second. Calculate the maximum restoring torque generated in the string under undamped conditions. (π² ≈ 31)

Two parallel S.H.M.s represented by x_{1} = 5sin(4πt + π / 3) cm and x_{2} =3 sin (4πt + π / 4) cm are superposed on a particle. Determine the amplitude and epoch of the resultant S.H.Μ.

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.

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