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

Answer

C

Explanation

Given, `y_(1)=a sin omega t and y_(2)=b cos omega t = b sin (omega t + (pi)/(2))`
The resultant displacement is given by
`y = y_(1)+y_(2)=sqrt(a^(2)+b^(2))sin (omega t + phi)`
Hence, the motion of superimposed wave is simple harmonic with amplitude `sqrt(a^(2)+b^(2))`