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Question

Three simple harmonic motions of equal amplitude 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.

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Solution

It is given that three S.H.M.s of equal amplitudes A and equal time periods are combined in the same direction.

Let Y1, Y2 and Y3 be the three vectors representing the motions, as shown in the figure given below.

According to the question:
Angle betweenY1 and Y2 = 60 °Angle between Y2 and Y3 = 60 °.


By using the vector method, we can find the resultant vector.
Resultant amplitude = Vector sum of the three vectors
= A + A cos 60° + A cos 60°
=A+A2+A2=2A

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