# Homework Help: Differential Equations: Is there Damping?

1. Jun 23, 2010

### undrcvrbro

1. The problem statement, all variables and given/known data

A spring mass system has the equation of motion:

c1e^(-t)*sin(t) + c2e^(-t)*cos(t) + 3*sin(t)

Is there damping in the system? Is there resonance in the system?

3. The attempt at a solution
If I had to guess I would say that the 3*sin(t) at the end of the equation would give it resonance because of the periodic motion of the sin function.

Also--this is also a guess-- there could be damping that's caused by the negative exponents on both of the exponentials. The graph for e^(-t) decreases to zero, so maybe that signifies how the movement of the spring is constantly being counteracted by the force of friction until eventually it comes to rest.

Then again, I could be completely wrong. I'm only typing this so that you know I'm giving it a shot. Can someone please help me out here. Obviously, my answers are wrong!

Thanks in advance for any help!

2. Jun 24, 2010

### undrcvrbro

Bump.

Anyone?

3. Jun 24, 2010

### HallsofIvy

Yes, there is damping because, as you say, there are negative exponents. There is no resonance because no part of the solution gets large for large t.