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Equation of motion for a particle perfor...

Equation of motion for a particle performing damped harmonic oscillation is given as `x=e^(-1t) cos(10pit+phi)`. The time when amplitude will half of the initial is :

Text Solution

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Amplitude of vibration at time t=0 is given by
`A=A_(0)e^(-0.1xx0)=1xxA_(0)=A_(0)`
also at `t=t` if `A=(A_(0))/2`
`implies1/2=e^(-0.1t)`
t=10 In 2=7s
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