Finding a Second-Order Differential Equation

[JNBirDy]

Homework Statement

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.

Homework Equations

E = U + K

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.

 

[Dick]

d/dt (cos(theta))=(-sin(theta))*d(theta)/dt. That's the chain rule.

 

[JNBirDy]

d/dt (cos(theta))=(-sin(theta))*d(theta)/dt. That's the chain rule.

Yes, thank you, I figured it out this morning. Silly mistake...