The amplitude of a particle due to superposition of the SHMs along the same line, X 1 = 2 sin 50 π t , X 2 = 10 sin ( 50 π t + 3 7 ∘ ) , X 3 = − 4 sin 50 π t , X 4 = − 12 cos 50 π t is:

Question

The amplitude of a particle due to superposition of the SHMs along the same line, X 1 ​ = 2 sin 50 π t , X 2 ​ = 10 sin ( 50 π t + 3 7 ∘ ) , X 3 ​ = − 4 sin 50 π t , X 4 ​ = − 12 cos 50 π t is:

TestHub · Accepted Answer

Sine part: 2 + 10 cos 3 7 ∘ − 4 = 2 + 8 − 4 = 6 . Cosine part: 10 sin 3 7 ∘ − 12 = 6 − 12 = − 6 . Amplitude = 36 + 36 ​ = 6 2 ​ .

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