Analogous Oscillations of a Pendulum and Liquid in a U-Tube

time

pendulum length

L/2

3.25

displacement from equilibrium

x

0.3

Period (sec)

1.99696

The simple harmonic motion for a liquid in a U-tube and a simple pendulum as proposed by Newton in his Principia Mathematica is animated in this Demonstration, with similar design and constraints (no friction) as in Newton's original work. All units are imperial. The energy level plot on the left is the water's energy; however, the timing is also for the pendulum. The clock

t=0

starts with motion already in progress at the displacement position for maximum kinetic energy for both the water and the pendulum. The assumed initial condition would be pressure on side

M

of the tube, causing displacement from equilibrium of

AB

and

CD

to a variable distance

x

at

EF

and

GH

; then the pressure is released to allow the water to move.