Out of the following functions representing motion of a particle which represents SHM
I. `y = sin omega t - cos omega t`
II. `y = sin^(3)omega t`
III. `y = 5 cos ((3 pi)/(4)-3 omega t)`
IV. `y = 1 + omega t + omega^(2)t^(2)`

Options

A. Only (IV) does not represent SHM
B. (I) and (III)
C. (I) and (II)
D. Only (I)

Answer

B

Explanation

For a simple harmonic motion `(d^(2)y)/(dt^(2)) alpha - y`
Hence, equation `y = sin omega t - cos omega t and y = 5 cos ((3pi)/(4) - 3 omega t)` are satisfying this condition and equation `y = 1 + omega t + omega^(2) t^(2)` is not period ic and `y = sin^(3) omega t` is periodic but not SHM.