The equations of two SHMs are `x_(1)=Asin(omegat+delta_(1))andx_(2)=Asin(omegat+delta_(2))` respectively. They superimpose on each other. Find the amplitude of the resultant.

Explanation

Resultant,
`x=x_(1)+x_(2)`
`=A[sin(omegat+delta_(1))+sin(omegat+delta_(2))]`
`=2A"sin"((omegat+delta_(1))+(omegat+delta_(2)))/2"cos"((omegat+delta_(1))-(omegat+delta_(2)))/2`
`=2A"cos"(delta_(1)-delta_(2))/2"sin"(omegat+(delta_(1)+delta_(2))/2)`
`therefore" "` Amplitude of the resultant SHM is `2A"cos"(delta_(1)-delta_(2))/2`.