# Homework Help: Leaky bucket in SHM

1. Aug 13, 2013

### PsychonautQQ

1. The problem statement, all variables and given/known data
There is a bucket with a leak in it in verticle SHM. What is the rate that the period changes with time?
dm/dt = 2 g/s
bucket = 2 kg
total water = 10kg
starting amplitude = 3cm
k=125 N/m

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

3. The attempt at a solution

dT/dt = 2pi * sqrt((dm/dt)/k)
dT/dt = 2pi * (dm/dt)^1/2 / k^(1/2)
dT/dt = 2pi * (m/2)^-1/2 / k^1/2
dT/dt = 2pi * (m2k)^-1/2

my calculus isn't the sharpest so I probably screwed up taking the derivative?

2. Aug 13, 2013

### TheShrike

Yeah, I think you did. Take a look at the first line again. You clearly know $\sqrt{A}=A^{\frac{1}{2}}$, so perhaps make that conversion for $T$ before taking the derivative. Also, you will need the chain rule for this problem.

3. Aug 13, 2013

### rude man

What does this mean? Units have to be kg/s, not g/s.