1.

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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