A particle is subjected to two simple harmonic motion in the same direction having equal amplitudes and equal frequency. If the resultant amplitude is equal to the amplitude of the individual motions. Find the phase difference between the individual motions.

Options

A. `(2pi)/(3)`
B. `(pi)/(3)`
C. `(pi)/(sqrt(3))`
D. `(2pi)/(sqrt(3))`

Answer

A

Explanation

Let the amplitude of the individual motion be A each The resulting apmlitude is also A If the phase difference between two motion is `delta`.
`A = sqrt(A^(2) +A^(2)+ 2A.A cos delta) = A sqrt(2(1 + cos delta))`
`= 2A cos delta/(2)`
`cos delta/(2) = (1)/(2) rArr delta = (2pi)/(3)`