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Finding a Second-Order Differential Equation

  1. Sep 21, 2011 #1
    1. The problem statement, all variables and given/known data
    A rotating objects motion can be described by its angle (θ). Given that an objects potential energy is U = 100(1-cosθ) and its kinetic energy is K = 10(dθ/dt)^2, form a second-order differential equation. Note that Total Energy = P + K, and that total energy does not change w.r.t. time.

    2. Relevant equations

    E = U + K

    3. The attempt at a solution

    E= 100(1-cosθ) + 10(dθ/dt)^2
    d(E)/dt = d/dt (100(1-cosθ)) + d/dt (10(dθ/dt)^2)
    0 = 100sinθ + 20(dθ/dt)(d^2θ/dt^2)
    -100sinθ = 20(dθ/dt)(d^2θ/dt^2)
    -5sinθ =(dθ/dt)(d^2θ/dt^2)

    Hmm.. the answer should be -5sinθ = d^2θ/dt^2. What am I doing wrong? Any help would be appreciated.
  2. jcsd
  3. Sep 21, 2011 #2


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    Homework Helper

    d/dt (cos(theta))=(-sin(theta))*d(theta)/dt. That's the chain rule.
  4. Sep 22, 2011 #3
    Yes, thank you, I figured it out this morning. Silly mistake...
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