A circular cylinder of mass m and radius r is connected by a spring of modulus K as shown. If it is free to roll in the rough horizontal surface without slipping, what will be its natural frequency?
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et us say in displaced position, the axis of cylinder is at a distance x from its mean position and its velocity of center of mass if x and angular velocity is. Then, as cylinder is not slipping. In this position the spring elongates by x. Using energy method we can find frequency of oscillation very easily. <br> Total energy of oscillation is <br><br> We have, so<br>constant <br> Comparing withconstant <br> So,
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