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Question

For the damped oscillator shown in Fig, the mass of the block is 200 g,k=80 N m1 and the damping constant b is 40 g s1 Calculate.
(a) The period of oscillation,
(b) Time period for its amplitude of vibrations to drop to half of its initial value
(c) The time for the mechanical energy to drop to half initial value.
766801_40c1d72f2fbd48429b5332ddaee99900.png

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Solution

For damped oscillation,
(a)T=2πωT=2πKm(l2m)2T=2×3.1480×1000200(40×10001000×2×200)2T=6.284001100T=0.314s
(b)F×A2
If amplitude gets reduced to half the force will reduce to one fourth.
Faaω2
So ω will become half.
T=2πωT=2×0.314=0.628s

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