Differential Equations: Is there Damping?

[undrcvrbro]

Homework Statement

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?

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!

 

[undrcvrbro]

Bump.

Anyone?

 

[HallsofIvy]

Homework Statement

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?

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!

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.