The resulting amplitude `A'` and the vebrations `S = A cos (omega t) + (A)/(2) cos (omega t + (pi)/(2)) xx (A)/(4) cos (omega t + pi)`
`= (A)/(8) cos (omega t+ (3pi)/(2)) = A' cos (omega t + delta)`
are…and…respectively.

Options

A. `sqrt(5)/(8) A, tan^(-1) ((1)/(2))`
B. `(3sqrt(5))/(8) A, tan^(-1) ((1)/(2))`
C. `(3sqrt(5))/(8) A, tan^(-1) ((1)/(4))`
D. `(1)/(2)R`

Answer

B

Explanation

`tan theta = (1)/(2)`

`A_("net") = sqrt(((3A)/(4))^(2) + ((3A)/(8))^(2)) = (3A)/(4) sqrt(1+ ((1)/(2))^(2)) = (3sqrt(5))/(8) A`