The displacement of a particle is given by ` x = 3 sin ( 5 pi t) + 4 cos ( 5 pi t)`. The amplitude of particle is

Options

A. 4
B. 5
C. 3
D. 7

Answer

B

Explanation

For the given super imposing waves
`A_(1) = 3, A_(2) = 4` and phase difference `phi = (pi)/(2)`
`A = sqrt(A_(1)^(2) + A_(2)^(2) + 2A_(1) A_(2) cos pi//2)`
`= sqrt((3)^(2) + (4)^(2)) = 5`