Question

obtain the equation of acceleration,velocity and displacement from the differential equation of linear S.H.M​

Answer 1

Answer:

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Answer 2

Explanation:

Displacement x = A cos ( ωt + Φ )

Velocity v = dx/dt = d/dt ( A cos ( ωt + Φ ) )                                                since, d/dt cos ( ωt + Φ ) = - sin ( ωt + Φ )

              v = - Aω sin ( ωt + Φ )

Acceleration a = dv/dt = d/dt ( - A sin ( ωt + Φ ) )

                     a = - Aω d/dt ( sin ( ωt + Φ ) )                                                 since, d/dt  sin (ωt + Φ ) = cos ( ωt + Φ )

                     a = - Aω² cos ( ωt + Φ )