Question 99: Oscillations

Question

The displacement of a damped harmonic
oscillator is given by
x(t ) = e
–0.1t
cos (10$$\pi $$t + f).
Here t is in seconds.
The time taken for its amplitude of vibration to
drop to half of its initial value is close to :

Accepted Answer

Amplitude at (t = 0) A
0
= e
Ã¢ÂÂ0.1ÃÂ 0
= 1
$$ 	herefore $$ $$at\,t = t$$     if $$A = {{{A_0}} \over 2}$$
$$ \Rightarrow $$ $${1 \over 2} = {e^{ - 0.1t}}$$
t = 10 ln 2  = 7 s

Answer

27 s

Answer

13 s

Answer

7 s

Answer

4 s

Oscillations

The displacement of a damped harmonic oscillator is given by x(t ) = e –0.1t cos (10$\pi $t + f). Here t is in seconds. The time taken for its amplitude of vibration to drop to half of its initial value is close to :

Choose the correct answer: