(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A 2kg bucket containing 10kg of water is hanging from a vertical ideal spring of force constant 125N/m and oscillating up and down with amplitude 3cm. Suddenly the bucket springs a leak in the bottom such that water drops out of the bucket at a steady rate of 2g/s.

2. Relevant equations

When the bucket is half full find the period of oscillation.

3. The attempt at a solution

What confuses me about this problem is that book solutions manual simply find the mass of the half full bucket (7kg) and plugs to the equation T = 2pi*sqrt(m/k).

What I initially tried to do is write the general equation of 2nd Newtons law:

dp/dt = -kx => x''m + x'm' + kx = 0, where x' means a derivative with respect of time.

And this is basically the equation with exact form as equation for damped oscillations. It only has replaced damping constant with m'. And it oscillates with frequency

ω' = √[k/m-(1/2m*dm/dt)^2]

However. the book assumes that the angular frequency is ω=√[k/m]

The answers in both cases agree with 5 significant figures, this is because dm/dt is very small. But in the case of dm/dt is significantly big, is this is the right way to attack this kind of problem?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Oscillating bucket, variable mass

**Physics Forums | Science Articles, Homework Help, Discussion**