Bikash T. Magar

From figure it can be noted that amplitude decreases exponentially which is the case for a damped oscillation,

A undamped oscillation isn't acted by any opposing force meaning it oscillates indefinitely.

But a damped oscillation is acted by another opposing force of damping constant b which is what we see in our daily life.

where,tau is damping time constant that is the time taken to decrease exponentially by 1/e of its initial value and

Since, the mechanical engineers doesn't want unwanted and...

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Solution:

Let m be the mass of the copper rod, g be the acceleration due to gravity and A be the cross-sectional area. It is given that L is the length of the rod then assume e to be the elongation produced. If Y be the Young's modulus of elasticity of copper, then

Y = FL/Ae

e = FL/AY

Further, F = mg and centre of mass of the rod is at the centre, so L' = L/2

Therefore, e = mgL/2AY