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A particle of mass 0.1 kg is executing S...

A particle of mass 0.1 kg is executing SHM of amplitude 0.1 m . When the particle passes through the mean position , its KE is `8 xx 10^(-3)` J. Find the equation of motion of the particle if the initial phase of oscillation is `45^(@)`

A

`y = 0.1sin(pm 4t + (pi)/(4))`

B

`y = 0.2sin(pm 4t + (pi)/(4))`

C

`y = 0.1sin(pm2t + (pi)/(4))`

D

`y = 0.2sin(pm2t + (pi)/(4))`

Text Solution

Verified by Experts

The correct Answer is:
A
The displacement of a particle in S.H.M. is given by
`y a = sin (omega t + phi)`
velcoity `= (dt)/(dy) = omega a cos (omegat + phi)`
The velocityis maximum when the particle passes through the mean position i.e.,
`((dy)/(dt))_(max) = omega a`
The kinetic energy at this instant is given by
`(1)/(2)m ((dy)/(dt))_(max)^(2)= (1)/(2) m omega^(2) a^(2) = 8 xx 10^(-3)` joule .
or `(1)/(2) xx (0.1) omega^(2) (0.1)^(2) = 8 xx 10^(-3)`
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