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  • What is the ratio of maximum acceleration to the maximum velocity of a simple harmonic oscillator?

What is the ratio of maximum acceleration to the maximum velocity of a simple harmonic oscillator?

Answers (1)

Let us consider x = A \sin \omega t to be an SHM

Now, v = \frac{dx}{dt}

            = A\omega \cos \omega t

Now, for v_{max},\cos \omega t = -1

Thus, v_{max} = A \omega

Now, a = \frac{dv}{dt}

          = -A\omega ^{2} \sin \omega t

Now, for a_{max},

\sin \omega t = -1

Thus, a_{max} = A\omega ^{2}

Now, \frac{a_{max}}{v_{max}} = \frac{A\omega ^{2}}{A\omega }

                        =\omega.

Posted by

infoexpert24

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