A uniform stick of mass M and length L is pivoted at its centre. Its ends are tied to two springs each of force constant K. In the position shown in figure, the strings are in their natural length. When the string is displaced through a small angle θ and released. The stick:

Question

A uniform stick of mass M and length L is pivoted at its centre. Its ends are tied to two springs each of force constant K. In the position shown in figure, the strings are in their natural length. When the string is displaced through a small angle θ and released. The stick:

Infinity Learn · Accepted Answer

If stick is rotated through a small angle θ, the spring is stretched by a distance $$L2$$θ. Therefore restoring force is spring $$=$$ $$K(L2$$θ$$)$$. Each spring causes a torque τ$$(=$$ $$Fd)$$ $$=(KL$$θ$$2)L2$$ in the same direction. Therefore equation of rotational motion isτ $$=$$ Iα$$-2(KL$$θ$$2)L2$$ $$=$$ Iα with I $$=$$ $$ML212$$α $$=$$ $$-(6KM)$$θStandard equation of angular S.H.M. is α $$=$$ $$-$$ω$$2$$θω$$2$$ $$=$$ $$6KMfrequency$$ f $$=$$ ω$$2$$π $$=12$$$$π$$$$6KM$$

A uniform stick of mass M and length L is pivoted at its centre. Its ends are tied to two springs each of force constant K. In the position shown in figure, the strings are in their natural length. When the string is displaced through a small angle $θ$ and released. The stick:

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