A particle is subjected to two simple harmonic motions 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.

Answer

A: 7cm

B: 6.1cm

C: 5cm

Explanation

The particle is subjected to two SHMs of same time period in the same direction.
Given `r_1=3`cm, `r_2=4`cm
and `phi`=phase difference
Resultant amplitude
`R=sqrt(r_1^2+r_2^2+2r_1r_2cos phi)`
a. when `phi=0^@`
`R=sqrt((3^2+4^2+2.3.4cos0^/2))`
`=sqrt49=7cm`
b. when `phi=60^@`
`R=sqrt((3^2+4^2+2.3.4cos60^@))`
`=sqrt37=6.1cm`
c. when `phi=90^@`
`R=sqrt((3^2+4^2+2.3.4cos90^@))`
`=sqrt25=5cm`