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Oscillations Spring constant newton's second law

  1. Apr 19, 2010 #1
    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?

  2. jcsd
  3. Apr 19, 2010 #2


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    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
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