1.

If x = a cos ωt + b sin ωt, show that it represents SHM.

Answer»

x = a cos ωt + b sin ωt

Now, \(\frac{dx}{dt}\) = – aω sinωt + bω cosωt

\(\frac{d^2x}{dt^2}\) = – aω2 cos ωt + bω2 sin ωt

⇒ \(\frac{d^2x}{dt^2}\) = – ω2 (a cos ωt+ b sin ωt)

⇒ \(\frac{d^2x}{dt^2}\) = – ω2x

⇒ α = – ω2x

Hence an SHM


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