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In damped oscillations, the amplitude of...

In damped oscillations, the amplitude of oscillations is reduced to one-fourth of its initial value 10cm at the end of 50 oscillations. What will be its amplitude when the oscillator completes 150 oscillations ?

A

`0.078cm`

B

`0.156 cm`

C

`0.312cm`

D

`0.122 cm`

Text Solution

Verified by Experts

The correct Answer is:
B
As, `a=a_(0)e^(-bt)`
Let `T` be the time priod of oscillation, then
Case (I),
`(a_(0))/(4)=a_(0)e^(-bxx50T)` or `(1)/(4)=e^(-50bT)`
Case (II),
`a=a_(0)e^(-bx150T)=a_(0)(e^(-50bT))^(3)=a_(0)((1)/(4))^(1//3)`
`=10((1)/(64))=0.156cm`
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