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I have the question

A piston in a car engine executes simple harmonic motion. The acceleration $a$ of the piston is related to its displacement $X$ by: $$a = -6.4 \times 10^5X.$$ Calculate the frequency of the motion.

I know that frequency is $f = 1/T$. However I am not sure how to use the information given to find the frequency.

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1 Answer

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$ a = - \omega^2x $

Proof at : (Look at the acceleration section)

Hence we know that

$ \omega^2 = 6.4 *10^5 $

$ \omega=800 $

and...

$$ \omega = 2\pi f $$ $$ f = \frac {\omega}{2\pi} = 127.323954474 $$

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