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 + sin 2 omega t`
D. `sin omega t - sin 2 omega t`

Answer

A

Explanation

One of the conditions for `SHM` is that restoring force (F) and hence acceleration (a) should be alphaortional to displacement (y).
Let, `y = sin omega t - cos omega t`
`(dy)/(dx) = 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`.