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Homework Help: Differential Equations: Is there Damping?

  1. Jun 23, 2010 #1
    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. jcsd
  3. Jun 24, 2010 #2

  4. Jun 24, 2010 #3


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    Science Advisor

    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.
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