Out of the following function reporesenting motion of a particle which represent `SHM`
(i) ` y = sin omega t - cos omega t `
(ii) `y = sin^(3) omega t`
(iii)`y =5cos ((3pi)/(4) - 3omega t)`
(iv) ` y = 1+ omega t + omega^(2) t^(2) `

Options

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

Answer

D

Explanation

For SHM, necessary condition `aprop-y`
(b) `y=sin^3omegat=(4sin^3omegat)/(4)=(3sinomegat-sinomegat)/(4)`
`v=(dy)/(dt)=(3cos omegat*omega-cos 3omegat*3omega)/(4)`
`a=(dv)/(dt)=(d^2y)/(dt)=(-3omega^2sinomegat+9omega^2sin3omegat)/(4)`
`=((3sinomegat+9sinomegat)/(4))`
`a!=-omega^2y` No SHM
(d) `y=1+omegat+omega^2t^2`
`v=(dy)/(dt)=omega+2omega^2t`
`a=(dv)/(dt)=2omega^2=a const ant`
`a!=-omega^2y`, No SHM