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Question

A particle is subjected to two simple harmonic motions, one along the X-axis and the other on a line making an angle

45 with the X-axis. The two motions are given by x=x0 sin ωt  and  s=s0 sin ωt

Find the amplitude of the resultant motion.


Solution

The particle is subjected to two simple harmonic motions represented by

x=x0 sin wt

x=s0 sin wt

and angle between two motions

=θ=45

  Resultant motions will be given by

R=(x2+s2+2xs.cos 45)

={x20 sin2 wt+s20 sin2 wt+2x0s0 sin2 ωt(12)}

=[x20+s20+2x0s0]1/2 sin ωt

  Resultant amplitude

[x20+s20+2x0s0]1/2


Physics

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