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-

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Standard XI

Physics

Springs in Parallel and Series

Three simple ...

Question

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

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$\frac{A}{2}$

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Solution

The correct option is A
2A

Three SHMs of equal amplitudes 'A' and equal time periods in the same direction combine. The vectors representing the three SHMs are shown it the figure.

Using vector method,

Resultant amplitude = Vector sum of the three vectors

$= A + A c o s 60^{\circ} + A c o s 60^{\circ} = A + \frac{A}{2} + \frac{A}{2} = 2 A$

So the amplitude of the resultant motion is 2A

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