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A particle starts simple harmonic motion...

A particle starts simple harmonic motion from the mean position. Its amplitude is a and total energy E . At one instant its kinetic energy is 3E/4 . Its displacement at that instant is

A

`(a)/(sqrt(2))`

B

`(a)/(2)`

C

`sqrt(3)(a)/(2)`

D

zero

Text Solution

Verified by Experts

The correct Answer is:
B
(b) `(K)/(E)=((1)/(2)momega^(2)(a^(2)-y^(2)))/((1)/(2)momega^(2)a^(2))=(a^(2)-y^(2))/(a^(2))=1-(y^(2))/(a^(2))`
So, `(((3E)/(4)))/(E)=1-(y^(2))/(a^(2))implies(y^(2))/(a^(2))=1-(3)/(4)=(1)/(4)implies y=(a)/(2)`
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