The amplitude of a damped oscillator decreases to 0.9 times its original magnitude in 5s. In another 10s it will decrease to α times its original magnitude, where α equals :

Question

The amplitude of a damped oscillator decreases to 0.9 times its original magnitude in 5s. In another 10s it will decrease to &#945; times its original magnitude, where &#945; equals :

Aicharya · Accepted Answer

A = A 0 &#160;e - bt 2 m After 5 second 0.9 A 0 = A 0 &#160;e - b 5 2 m ...... (i) After 10 more second A = A 0 &#160;e - b 1 5 2 m ...... (ii) From (i) and (ii) A = 0.729 A 0

The amplitude of a damped oscillator decreases to 0.9 times its original magnitude in 5s. In another 10s it…

Solution