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The linear displacement (y) of a particl...

The linear displacement (y) of a particle varies with time as `y = (a sin omega t + b cos omega t)`. State whether the particle is executing SHM or not.

Text Solution

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Yes, the particle is performing SHM. Since `d^(2)y//dt^(2)` = acceleration of the particle, we get, differentiating the given expression twice
`(d^(2)y)/(dt^(2)) = - omega^(2) (a sin omega t + b cos omega t) = - omega^(2) (y)`
`rArr a prop - y`
`rArr " force " F (= ma) prop - y`
which is the necessary and sufficient condition for SHM.
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