Which of the following functionss represents a simple harmonic oscillation ?

Options

A. `sin omega t - cos omega t`
B. `sin^(2) omega t`
C. `sin omega t + sin2 omega t`
D. `sin omega t - sin 2 omega t`

Answer

A

Explanation

Let `y = sin omega t - cos omega t`
`(dv)/(dt) = omega cos omega t + omega sin omega t`
`(d^(2)y)/(dt^(2)) = - omega^(2)sin omega t + omega^(2) cos omega t`
`or a = -omega^(2)(sin omega t - cos omega t)`
`a = - omega^(2)y`
`rArr a prop -y`
This satsfied the condition of `SHM` other equations do not Hence `sin omega t - cos omega t` represents `SHM`