Three simple harmonic motions of equal amplitudes A and equal time periods in the same direction combine. The phase of the second motion is `60^@` ahead of the first and the phase of the third motion is `60^@` ahead of the second. Find the amplitude of the resultant motion.

Answer

A, B

Explanation

Three SHMs of equal amplitudes AS and equal time period in the same direction cobine. The vectors representing the three SHMs are shown in the ure using vector method.

Resultant ampllitude
=vector sum of the three vectors
`=A+acos60^@+Acos60^@`
`=A+A/2+A/2=2a`
So, the amplitude of the resultant motion is 2A.