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If y = a sin wt + b cos wt, does it represent S.H.M.? What is the amplitude of motion? What is the length of the path? |
Answer» y = a sin wt + b cos wt a = r cosθ and b = r sinθ y = r sin(wt = θ) ....(i) a2 + b2 = r2(sin2θ + cos2θ) = r2 or, r = √{a2 + b2} (taking positive sign) Putting this value in (i), we have y = √{(a2 + b2) sin (wt = θ)} Therefore the given equation represents a S.H.M. Amplitude of motion, r = √{a2 + b2} Length of the path, 2r = 2√{(a2 + b2)} |
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