Mastering Simple and Physical Pendulum Motion with Newton's Laws and Hooke's Law

[bluejay27]

Revisiting my general physics notes, I noticed that you just need Newton's second law and knowing Hooke's law to predicting the motion of a simple pendulum and that of a physical pendulum. For the simple pendulum, simply consider the tangential component of the force with some trig expressions such as the small angle approximation sin(theta) = theta and theta = x/L where x is the distance covered and L the length of the pendulum. For the physical pendulum, just used Newton's 2nd law in terms of torque.Is there anything else that you think I am missing?

 

[hilbert2]

The pendulum motion obeys Hooke's law only if you make the small-amplitude approximation ($\sin \theta \approx \theta$). If the motion goes through something like a 60 degree angle, you need elliptic functions to write down the trajectory of the system.