A particle is subjected to two `SHMs ` `x_(1) = A_(1) sin omegat` and `x_(2) = A_(2)sin (omegat +(pi)/(4))`. The resultant `SHM` will have an amplitude of

Options

A. `(A_(1) + A_(2))/(2)`
B. `sqrt(A_(1)^(2) + A_(2)^(2))`
C. `sqrt(A_(1)^(2) + A_(2)^(2) + sqrt(2) A_(1) A_(2))`
D. `A_(1) A_(2)`

Answer

C

Explanation

`A_(res) = sqrt(A_(1)^(2) + A_(2)^(2) + 2A_(1) A_(2) cos ((pi)/(4))) = sqrt(A_(1)^(2) + A_(2)^(2) + sqrt(2) A_(1) A_(2))`