A block of mass m has two similar rubber ribb | vedclass

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(C) When the block is displaced by a distance $x$ from the mean position,one of the rubber ribbons gets stretched by $x$,while the other ribbon become

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$2\pi \sqrt {\frac{m}{k}} $

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(C) When the block is displaced by a distance $x$ from the mean position,one of the rubber ribbons gets stretched by $x$,while the other ribbon becomes slack and does not exert any force,because rubber ribbons cannot be compressed like springs.The restoring force acting on the block is $F = Kx$.Using Newton's second law,$ma = Kx$,which gives the acceleration $a = \frac{Kx}{m}$.Comparing this with the standard equation for simple harmonic motion $a = \omega^2 x$,we get $\omega^2 = \frac{K}{m}$,or $\omega = \sqrt{\frac{K}{m}}$.The time period $T$ of vibration is given by $T = \frac{2\pi}{\omega}$.Substituting the value of $\omega$,we get $T = 2\pi \sqrt{\frac{m}{K}}$.

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