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

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

Grade:11

2 Answers

Saurabh Koranglekar
askIITians Faculty 10341 Points
one year ago
576-1068_21.PNG
Vikas TU
14149 Points
one year ago
Amplitude of damped oscillation
a=a0e^(−bt/2m)
As, a=0.90a0,t=5s, so
0.9a0=a0e^(−bt/2m) or 0.9=e^(−5b/2m) …(i)
When t=5+10=15s,a=xa0, then
xa0=a0e^(−b×15/2m)
or x=[e^(−5b/2m)]^3 = (0.9)3=0.729

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