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A particle undergoing simle harmonic mot...

A particle undergoing simle harmonic motion has time dependent displacement given by `x(t)=Asin (pi t)/(90)`.The ratio of kinetic to potential energy of this partle at t= 210s will be :

A

`(1)/(9)`

B

1

C

`(1)/(3)`

D

2

Text Solution

Verified by Experts

The correct Answer is:
C
`x|_(t = 210)= A sin [ ((pi)/(90)) xx 210] = a sin (2 pi + (pi)/( 3)) = ( sqrt(3) A)/(2)`
P.E. `(V) = (1)/(2) kx ^(2) = (1)/(2) k (( 3A^(2))/(4))`
K.E. `(T) = (1)/(2) mv^(2) = (1)/(2) m omega ^(2) (1)/(2) m omega^(2) ( sqrt(A^(2) - ( 3A^(2))/(4)))^(2)`
`= (1)/(2) (KA^(2))/( 4)`
`:.` Required ratio ` (T)/(U) = (1)/(3)`
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