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## Homework Statement

A 1.60 kg, horizontal, uniform tray is attached to a vertical ideal spring of force constant 195 N/m and a 280 g metal ball is in the tray. The spring is below the tray, so it can oscillate up-and-down. The tray is then pushed down 15.0 cm below its equilibrium point (call this point A) and released from rest.

a) How high above point A will the tray be when the metal ball leaves the tray? (Hint: This does not occur when the ball and tray reach their maximum speeds.)

b) How much time elapses between releasing the system at point A and the ball leaving the tray?

c) How fast is the ball moving just as it leaves the tray?

## Homework Equations

a

_{max}=Aω

^{2}

x=Acos(ωt+[itex]\phi[/itex])

v=-ωAsin(ωt+[itex]\phi[/itex])

## The Attempt at a Solution

So I already solved part (a) by equating the accelerations of the ball and the spring system, g=xω

^{2}, and got an answer for x. But I can't seem to figure out how to get the time at this instant for part (b): I tried using x=Acos(ωt+[itex]\phi[/itex]) and solving for t, but it doesn't make too much sense to me. And I believe I can solve for part (c) with the time t from part (b) using v=-ωAsin(ωt+[itex]\phi[/itex]), but this I'm also not 100 percent on.

Could anyone nudge me in the right direction? I seem to be stuck after part (a)

Thanks!