$14\mathrm{.}23$ CALC The jerk is defined to be the time rate of change of the acceleration. $($a$)$ If the velocity of an object undergoing SHM is given by

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$=$

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$$

$$

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sin

$($

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$)$

$,$

what is the equation for the x$-$component of the jerk as a function of time? $($b$)$ What is the value of

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for the object when the x$-$component of the jerk has its largest positive value? $($c$)$ What is

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when the x$-$component of the jerk is most negative? $($d$)$ When it is zero? $($e$)$ If

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equals

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$0\mathrm{.}040$

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s

$2$

times the x$-$component of the jerk for all

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$,$

what is the period of the motion?