Q.

The amplitude of a damped oscillations decreases to 0.9 times its initial value in 5 seconds. By how many times to its initial value, energy of oscillation decreases in first 10 seconds?

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a

0.81

b

0.73

c

0.95

d

0.66

answer is D.

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Detailed Solution

Amplitude of damped oscillator is given by A=A0e−bt2min 5 second 0.9A0=A0e−5b2m In 10 second , enregy is given by E=E0e−btm E=E0e−10bm⇒E=E0e−5bm2=E00.922=0.656E0 ⇒Energy ≈0.66E0
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