# Oscillations Spring constant newton's second law

1. Apr 19, 2010

### bfpri

So i have the equation m*(d2x/dt^2)+c*(dx/dt)+kx=0, where d2x/dt^2 is the second derivative.

So i'm given that m=10 kg, and k=28 N/m. At time t=0 the mass is displaced to x=.18m and then released from rest. I need to derive an expression for the displacement x and the velocity v of the mass as a function of time where
a) c=3 N-s/M
b) c=50 N-s/m

Since I have to do this in matlab, I attempted to solve with dsolve and got
C10/exp((t*(c - (c^2 - 4*k*m)^(1/2)))/(2*m)) - (C10 - 9/50)/exp((t*(c + (c^2 - 4*k*m)^(1/2)))/(2*m))

clearly not right..How do i set it up correctly so i can solve for both x and v?

Thanks

2. Apr 19, 2010

### vela

Staff Emeritus
Actually, that answer is probably right, but it obscures what's going on in the problem.

What's the characteristic equation you get for that differential equation, and what are its solutions? That's a good place to start. (I'm assuming, perhaps incorrectly, that you know how to solve this differential equation. If you don't, we can back up a bit.)

Last edited: Apr 19, 2010