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

Answer

A

Explanation

`A_(R) sqrt(A_(1)^(2) + A_(2)^(2) + 2A_(1)A_(2) cos phi)`
`phi` is the phase diff.
`phi = 90^(@), A_(1) = a, A_(2) = b`
`therefore A_(R) = sqrt(a^(2) + b^(2))`