Some types of forces have a special property for which the work performed by the force as an object moves from some starting point A to some ending point B is completely independent of the path of travel from A to B. The work only depends on the end points. Such forces are called conservative because they lead to (mechanical) energy conservation principles.

#### Theory

Students have heard about “conservation of energy.” However, it’s important to not that mechanical energy, generally, is not conserved. Here we discuss the the types of forces which do conserve mechanical energy.

#### Simple Pendulum

The first system we study is the simple pendulum:

If you wish to play with the pendulum simulation in the video above, go here. Keyboard keys 1, 2, 3, and 0 will toggle the energy bars. Key p will pause.

#### Springy Pendulum

Now we replace the pendulum rod with a spring. This leads to more interesting dynamics. Is the system still conservative?

If you wish to play with the pendulum simulation in the video above, go here. Keyboard keys 1, 2, 3, 4 and 0 will toggle the energy bars. Key p will pause.

#### Springy Pendulum with Damping

What is damping and what happens if we add it to the springy pendulum?

If you wish to play with the pendulum simulation in the video above, go here. Keyboard keys 1, 2, 3, 4 and 0 will toggle the energy bars. Key p will pause. Key d will turn on damping.

#### Sliding Springy Pendulum

What happens if we allow the base of the springy pendulum to slide horizontally on a frictionless rail? We get an extra “degree of freedom”. In what sense is this system conservative? And how can one use damping to tame the swaying motion of a tall building?

If you want to play with the springy pendulum with sliding base click here.

#### Double Pendulum

Coming soon, I hope. But if you want to play with it now, click here.