(adsbygoogle = window.adsbygoogle || []).push({}); 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=U+K

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.

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# Finding a Second-Order Differential Equation

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