InterviewSolution
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InterviewSolution
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The displacement of a particle executing periodic motion is given byy = 4 cos2 (t/2) sin x (1000 t)Find the independent constituent simple harmonic motions. |
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Answer» y = 4 cos2 (t/2) sin x (1000 t) = 2(1 + cost) sin (1000t)(2 cos2θ = 1 + cos 2θ) = 2 sin 1000 t + 2 sin 100 t x cos t = 2 sin 1000 t + (sin 1000 + 1)t + sin (1000 - 1)t [2 sin A cos A = sin(A + B) + sin(A - B)] = 2 sin 1000 t + sin 1001 t + sin 999t = sin 1000 t + sin 1000 t + sin 1001t + sin 999 t It shows that the given expression is composed of 4 SHMs out of which two are same. This means that the given expression is the result of three independent harmonics. |
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