The displacement of a damped harmonic oscillator is given by xt-e-01-1t cos 10- t- - Here t is in seconds- The time taken for its amplitude of vibration to drop to half for its initial value is close to -

The correct option is B 7s A=A_0e^ 0.1t=A_02 ln2=0.1t t=10ln2=6.93 ≈ 7 sec ...

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Standard XII

Physics

Simple Harmonic Oscillation

The displacem...

Question

The displacement of a damped harmonic oscillator is given by $x (t) = e^{- 01.1 t} c o s (10 π t + Φ) .$ Here $t$ is in seconds. The time taken for its amplitude of vibration to drop to half for its initial value is close to :

13 s

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7 s

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27 s

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4 s

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Solution

The correct option is B $7 s$
$A = A_{0} e^{- 0.1 t} = \frac{A_{0}}{2}$
$l n 2 = 0.1 t$
$t = 10 l n 2 = 6.93 \approx 7 s e c$

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The displacement of a damped harmonic oscillator is given by x(t)=e−01.1tcos(10πt+Φ). Here t is in seconds. The time taken for its amplitude of vibration to drop to half for its initial value is close to :

The correct option is B 7sA=A0e−0.1t=A02ln2=0.1tt=10ln2=6.93≈7sec

The displacement of a damped harmonic oscillator is given by $x (t) = e^{- 01.1 t} c o s (10 π t + Φ) .$ Here $t$ is in seconds. The time taken for its amplitude of vibration to drop to half for its initial value is close to :

The correct option is B $7 s$
$A = A_{0} e^{- 0.1 t} = \frac{A_{0}}{2}$
$l n 2 = 0.1 t$
$t = 10 l n 2 = 6.93 \approx 7 s e c$