How do you derive Vmax for a simple pendulum in terms of h,L,T and any necessary constants?

Question

Hi,

I need help on derivation of some intro physics equations regarding kinematics, pendulums, ideal gas laws, fluid density and angular velocity.

Answer 1

I assume that

V_max is maximal velocity,

h is maximal height of the pendulum above its lowest point,

L is the length of the pendulum,

T is the period.

V_max is achieved at the lowest point and depends only on h.

The reason is that all the potential energy at height h gets converted

to the kinetic energy at the lowest point.

Let

m be the mass of the pendulum,

g be gravitational acceleration.

Then the conservation of energy statement is

mgh = mV_max²/2

V_max = √(2gh)