A $0\mathrm{.}440-kg$ object attached to a spring with a force constant of $8\mathrm{.}00\frac{N}{m}$ vibrates in simple harmonic motion with an amplitude of $11\mathrm{.}2$ cm $.($Assume the position of the object is at the origin at $t=0.)$

$($a$)$ Calculate the maximum value of its speed.

Note that the amplitude is given in cm $,$ and the velocity is to be given in $c\frac{m}{s}.c\frac{m}{s}$

$($b$)$ Calculate the maximum value of its acceleration.

You may have calculated the acceleration correctly with an incorrect result for the angular velocity. Check your calculation of $.c\frac{m}{s^2}$

$($c$)$ Calculate the value of its speed when the object is $7\mathrm{.}20$ cm from the equilibrium position.

Can you determine a time when the object is at this position? You can then use this time in your equation of motion. $c\frac{m}{s}$

$($d$)$ Calculate the value of its acceleration when the object is $7\mathrm{.}20$ cm from the equilibrium position.

How can you determine the force that acts on the object at this position? $c\frac{m}{s^2}$

$($e$)$ Calculate the time interval required for the object to move from $x=0$ to $x=3\mathrm{.}20cm.$

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