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Suppose we have a block of unknown mass and a spring of unknown force constant. Show how we can predict the period of oscillation of this block – spring system simply by measuring the extension of the spring produced by attaching the block to it.

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5 years ago

```							Simple harmonic motion (SHM) is the motion in which the restoring force (F) is proportional to displacement (x) from the mean position and opposes its increase.So, F = kxHere, k is the force constant.The restoring force F acting on the body isF = mass × acceleration = maWhen the block of mass m is suspended with the spring, then at equilibrium position, the restoring force must be equal to the weight (mg) of the body.So,kx = mgk/m = g/xWe know that that angular velocity (w) is defined as,w = √k/mTo find out the angular velocity (w) in terms of g and x, substitute g/x for k/m in the equation w = √k/m,w = √k/m = √ g/xBut the time period (T) of the oscillation is defined as,T = 2π/ wTo find out the time period, substitute √ g/x for w in the equation T = 2π/ w,T = 2π/ w = 2π√x/gSo, by measuring the displacement of the spring when it is attached with a block of mass m and suspended freely, you can predict the period of oscillation of this block.
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5 years ago
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