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 1
B. Only (4) does not represent SHM
C. Only (1) and (3)
D. Only (1) and (2)

Answer

C

Explanation

`y=sinomegat-cosomegat`
`=sqrt(2)[(1)/(sqrt(2))sinomegat-(1)/(sqrt(2))cosomegat]=sqrt(2)sin(omegat-(pi)/(4))`
It represents a SHM with time period, `T=(2pi)/(omega)`
`y=sin^(3)omegat=(1)/(4)[3sinomegat-sin3omegat]`
represents a periodic motion with time period `T=(2pi)/(omega)` but not SHM.
`y=5cos((3pi)/(4)-3omegat)`
`=5cos(3omegat-(3pi)/(4))[because cos(-theta)=costheta]`
It represents a SHM with time period, `T=(2pi)/(3omega)`.
`y=1+omegat+omega^(2)r^(2)`
It represents a non-periodic motoin. Also it is not physically acceptable as the `yrarroo` as `trarroo`.