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

The two displacements equations are `y_(1)=a sin(omega t)`
and `y_(2)=b cos(omega t)=b sin(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 frequencies for both SHMs are same, resultant motion will be SHM.
Now `A_(eq)=sqrt(a^(2)+b^(2)+2ab cos""(pi)/(2))`
`impliesA_(eq)=sqrt(a^(2)+b^(2))`