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Two springs each of spring constant are attached to the sphere, one at centre and the other at the top as shown. The radius of the sphere is , and its mass is . If the sphere rolls on the ground without slipping, the angular frequency of oscillation of the sphere would be


(a)
(b)
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(d)

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Important Questions on Oscillations
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A simple pendulum is vertically hanging in a car. The mass of the bob is . If the car is given an acceleration suddenly, find the maximum displacement of the bob.


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What will be the momentum v/s position plot of a spring mass oscillator kept on a rough horizontal surface? What should be the plot for one cycle?

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A pendulum suspended from the roof of a railway carriage travelling at a speed around a curve of radius metres makes oscillations per second. If the same pendulum makes oscillations per second when the carriage is stationary, what is the value of ?

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A circular disc has a tiny hole in it, at a distance from its centre. Its mass is and radius . A horizontal shaft is passed through the hole and held fixed so that the disc can freely swing in the vertical plane. For small disturbance, the disc performs S.H.M. whose time period is minimum for

MEDIUM
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If the length of a simple pendulum is comparable to the radius of the earth, then find the time period for oscillation.

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The figure alongside shows a system of springs connected to a mass . The amplitude of oscillation of this system would be . What will be the ratio of the amplitudes of oscillation of points and ?


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A block of mass is attached to three springs, having force constants and as shown in the figure. If the block is slightly pushed against spring . Then find the frequency of oscillations,


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The right block in the figure moves at a speed towards the left block placed in equilibrium. All the surfaces are smooth and all the collisions are elastic. Find the time period of the motion.

