Solve SHM Leaky Bucket: dT/dt Calculus Solution

[PsychonautQQ]

Homework Statement

There is a bucket with a leak in it in vertical 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

Homework Equations

T=2pi*sqrt(m/k)

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?

 

[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.

 

[rude man]

dm/dt = 2 g/s

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