Out of the following functions representing motion of a particle which represent SHM?
(a) `y= sin omega t- cos omega t`
(b) `y= sin^(2) omega t`
(c ) `y= 5cos ((3pi)/(4)-3 omega t)`
(d) `y= 1+ omega t+ omega^(2) t^(2)`

Options

A. Only (a)
B. Only (d) does not represent SHM
C. Only (a) and (c )
D. Only (a) and (b)

Answer

C

Explanation

`y= sin omega t- cos omega t= sqrt(2) sin (omega t-(pi)/(4))`
and `y= 5 cos ((3pi)/(4)-3 omega t)`
`= 5cos (3 omega t- (3pi)/(4))`.
These equations represents a SHM with similar to the equation of displacement `y= A sin (omega t+x)`.