The mass starts from rest (initial kinetic energy is zero) an angle θ0 above the vertical: \[\begin{aligned} E&=mgL(1-\cos\theta)+\frac{1}{2}mv^2\\ E_{initial}&=mgL(1-\cos\theta_0)\end{align...The mass starts from rest (initial kinetic energy is zero) an angle θ0 above the vertical: E=mgL(1−cosθ)+12mv2Einitial=mgL(1−cosθ0) Now that we have found the total energy of the system, we can write our general expression for the energy of the system at any point: E=mgL(1−cosθ)+12mv2mgL(1−cosθ0)=mgL(1−cosθ)+12mv2 All that’s left to do is simplif…
