Question

Obtain differential equation for linear S.H.M​

Answer 1

Answer:

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Explanation:

The differential equation for the Simple harmonic motion has the following solutions:

x=A\sin \omega \,tx=Asinωt (This solution when the particle is in its mean position point (O) in figure (a)

{{x}_{0}}=A\sin \phix  

0

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=Asinϕ (When the particle is at the position & (not at mean position) in figure (b)

x=A\sin \left( \omega t+\phi \right)x=Asin(ωt+ϕ) (When the particle at Q at in figure (b) (any time t).

These solutions can be verified by substituting this x values in the above differential equation for the linear simple harmonic motion.