# ODE application of damped motion

1. Mar 24, 2013

### leroyjenkens

1. The problem statement, all variables and given/known data
A mass of 40 g stretches a spring 10 cm. A damping device imparts a resistance to motion numerically equal to 560 (measured in dynes/(cm/s)) times the instantaneous velocity. Find the equation of motion if the mass is released from the equilibrium position with a downward velocity of 2 cm/s.

2. Relevant equations

$\frac{d^2x}{dt^2}+\frac{β}{m}\frac{dx}{dt}+\frac{k}{m}x=0$

3. The attempt at a solution
The only thing I think that's stopping me from doing this problem is the units. I converted 40g to .04 kg, and 10 cm to 0.1 m. But I'm not sure what to do with the 560 dynes/(cm/s). Do I turn that into 56000 dynes/(m/s)? That seems like a huge number for β, considering I used 0.4 in the last problem for β.
Thanks.

2. Mar 24, 2013

### voko

In principle, you do not have to convert any units, all the given values are consistently in CGS.

But if you want to, then the resistance is indeed 56000 dynes per m/s, but you need to finish the conversion to newtons per m/s.