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

The two displacement equation are `y_(1) = a sin(omega t)` ltbrtgt and `y_(2) = b cos(omega t) = b(omega t + (pi)/(2))`
`y_(eq) = y_(1) + y_(2)`
`= a sin omega t + b cos omega t`
`= a sin omega t + b sin(omega t + (pi)/(2))`
Since the frequency for both `SHM` are same resultant motion will be `SHM`
Now `A_(eq) = sqrt(a^(2) +b^(2) + 2ab cos (pi)/(2))`
`rArr sqrt(a^(2) +b^(2))`