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

Here, `y_(1)=a sin omegat ` and
`y_(2)=b cos omega t =b sin (omegat+(pi)/(2))`
`A_(1)=a, A_(2)=b, phi=pi//2`j
Since the frequencies of both the displacements are same, resusltant motion will be SHM.
No amplitude `A=sqrt(A_(1)^(2)+A_(2)^(2)+2A_(1)A_(2)cosphi)`.
`:. A=sqrt(a^(2)+b^(2))`