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

Let `y = sin omega t - cos omega t`
`(dy)/(dt) = omega cos omegat + omega sin omega t`
`(d^(2)y)/(dt^(2))=-omega^(2)sin omega t + omega^(2) cos omega t`
or `a = - omega^(2) (sin t - cos omega t) or a = - omega^(2)y rArr a prop - y`
Thus, it is a simple harmonic motion, this condition does not satisfied with other functions.