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 `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

Resultant displacement-
`y=y_(1)+y_(2)=asin(omegat)+bcosomegat=Asin(omegat+phi)`
`A=sqrt(a^(2)+b^(2))`
Simple harmonic with amplitude `sqrt(a^(2)+b^(2))`.