Question

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

Answer 1

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