You want to study simple harmonic motion using an air track with a $180$g glider and a spring.

First, you measure the spring constant: When you extend the length of the spring by $25$ cm$,$ a force

sensor measures $4\mathrm{.}0$ N$.$ You observe also that the force measured is proportional to the

displacement of the spring from its equilibrium length.

You now attach one end of the spring to a fixed bracket on the air track and the other to the air

glider. You pull the glider to the right, thereby extending the spring by $32$ cm$,$ and release it from

rest.

Calculate the force constant of the spring. $(1$p$)$

Calculate the angular frequency of the oscillation of the air glider at the end of the spring. $(1$p$)$

Calculate the period of the oscillation. $(1$p$)$

Write the equation for the displacement $()()$ cosx t A t

$=+$ by substituting values for the

amplitude, angular acceleration, and phase angle. $(1$p$)$

Write the equation for the velocity as a function of time $()$v t for the motion of the oscillating glider.

$(1$p$)$

Calculate the maximum speed of the glider. $(1$p$)$