A 2.10kg bucket containing 13.0kg of water is hanging from a vertical ideal spri

Question

A 2.10kg bucket containing 13.0kg of water is hanging from a vertical ideal spring of force constant 120N/m and oscillating up and down with an amplitude of 3.00 cm. Suddenly the bucket springs a leak in the bottom such that water drops out at a steady rate of 2.00 g/s.

1)When the bucket is half full find the period of oscillation. Thus, T=...? s

2)When the bucket is half full find the rate at which the period is changing with respect to time. Thus, dT/dt= ...?

3)Is the period getting longer or shorter?

4)What is the shortest period this system can have? Thus, Tshortest= ....? s

Explanation / Answer

2. Relevant equations
T=2?sqrt(?m/k)


3. The attempt at a solution
I know that I need to find T as a function of t, then take the derivative wrt t and evaluate it at the time when the bucket is half full.
But I'm not sure how to set this up.. I tried:
T=2?sqrt[(m1+m2+?mt)/k]
where m1=2.1 kg, m2=13 kg, and ?m=0.02 kg/s

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