when two displacements represented by `y_(1) = a sin(omega t)` and `y_(2) = b cos (omega t)` are superimposed the motion is

Options

A. simple harmonic with amplitude `(a)/(b)`
B. simple harmonic with amplitude `sqrt(a^(2)+b^(2))`
C. simple harmonic with amplitude `((a+b))/(2)`
D. not a simple harmonic

Answer

B

Explanation

`y_(1)=a "sin" omega t`
`y_(2)=b "cos" omega t=b "sin" (omega t+(pi)/(2))`
`therefore` Phase difference `(phi)=(pi)/(2)`
`therefore` The resul"tan"t motion is also a S.H.M. of amplitude
`A = sqrt(A_(1)^(2)+A_(2)^(2)+2A_(1)A_(2) "cos" phi)`
` therefore A= sqrt(a^(2)+b^(2)+2ab "cos" (pi)/(2))=sqrt(a^(2)+b^(2))`