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Q.

The displacement of damped harmonic oscillator is given by  x(t)=e−0.1t cos(10πt+ϕ) here t is in seconds. The time taken for its amplitude of vibration to drop to half of its initial value is close to 

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a

13 s

b

7 s

c

27 s

d

4 s

answer is B.

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Detailed Solution

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For damped oscillation, amplitude is given as

A=A0e−0.1t      ⇒ln  2=0.1t      ⇒t=10ln2=6.93    ⇒≈7sec

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