The displacement of a particle varies with time according to the relation `y=a sin omega t +b cos omega t `.

Options

A. The motion is S.H.M. with amplitude `a^(2)+b^(2)`
B. The motion is S.H.M. with amplitude a+b
C. The motion is S.H.M. with amplitude `a^(2)+b^(2)`
D. The motion is S.H.M. with amplitude `sqrt(a^(2)+b^(2))`

Answer

D

Explanation

We can write
`y=sqrt(a^(2)+b^(2))sin(omegat+Delta)`
where `tan Delta=(b)/(a)`.