A body executing linear simple harmonic motion has a velocity of 3 cm/s when its displacement is 4 cm and a velocity of 4 cm/s when its displacement is 3 cm. Then amplitude of oscillation with be

Options

A. 5 cm
B. 7.5 cm
C. 10 cm
D. 12.5 cm

Answer

A

Explanation

`x=Asinomegat`
`12.5=25sinomegat`
`(1)/(2)=sinomegat " "thereforeomegat=sin^(-1)(0.5)`
`omegat=(pi)/(6)" "therefore (2pi)/(T)t=(pi)/(6)`
`t_(1)=(T)/(12)=(3)/(12)=(1)/(4)s`
One side of 12.5 cm time is 1/4 s
`therefore` Other side of 12.5 cm the time is 1/4 s
`therefore` The time for either sides of 12.5 cm from mean position is
`(1)/(4)+(1)/(4)=(1)/(2)=0.5s`