Consider a simple pendulum of mass m and length L. The pivot point of the pendulum is being moved vertically with a small amplitude a and frequency ω. If g is the acceleration due to gravity, then what would be the change in Hamiltonian equation in Lagrangian mechanics?
1
\(H = p_{\theta}^2 /(2mL^2) + mgL(1 - cos(\theta)) + \frac{1}{2} mω^2 a^2 cos^2(\theta)\)
2
\(H = p_{\theta}^2 /(2mL^2) + mgL(1 - cos(\theta)) + \frac{1}{2} mω^2 a^2 sin^2(ωt)\)
3
\(H = p_{\theta}^2 /(2mL^2) - mgL(1 - cos(\theta)) - \frac{1}{2} mω^2 a^2 cos^2(ωt)\)
4
\(H = p_{\theta}^2 /(2mL^2) + mgL(1 - cos(\theta))\)
5
Question Not Attempted