## Simple Harmonic Motion and Pendula

• ME17.3 Long Pendulum Hanging from Ceiling

This is mainly used for conservation of energy. This pendulum suspended from the ceiling with a long rope already attached to the first pillar on the right facing the class. A student volunteer feels the weight of the ball, then attaches it to the rope. He stands by the pillar and puts the ball to his nose. Then he lets go and remains in place. From his point of view, the ball will hit him in the face, but conservation of energy says that the ball will go no closer to his nose than it was when he let go.

• ME17.5 Pair of Pendula with Length Ratio 2:1

The two pendulums begin swinging together. They will fall out of synchronization but will meet every four times since frequency depends upon the square root of length.

• ME17.8 Parallel Spring Bucket

Various SHM experiments can be done with the bracket. Hang masses in ratio 2:1 fro springs with a spring constant in ratio 2:1 and demonstrate that the period is the same. Hang springs of different spring constants in series and parallel.

• ME17.9 Wilberforce Pendulum

This may be harder to see from the back of the room. The pendulum begins oscillating vertically, but the energy transfers between modes. The vertical oscillations have stopped and the weight spins with a maximum amplitude. After that point, energy begins to go transfer back to the vertical oscillation, and so the rotational oscillations dwindle.