 Simple pendulum

 
The period of a simple pendulum is calculated to the third term of the expansion, the height by trigonometry, and energetics from Newtonian equations.
 
The simple pendulum neglects contributions from the mass of the connecting rod, friction at the pivot point, and air resistance. Note that above small angles, the pendulum is not harmonic, and the first two anharmonic components are calculated here, making the result accurate to within 1% for angles of up to 30 degrees. Naturally the energy can only be calculated if the mass of the bob is provided, and the speed is zero unless a deflection angle greater than zero is used.  