Pendulum with Variable Plane of Oscillation

The top pictures show a standard rigid pendulum. The gravitational force F = mg is directed downward on the pendulum bob, and the restoring force on the bob is mg sinθ.

When the plane of oscillation is rotated about the horizontal axis by angle φ (bottom pictures), the gravitational force mg is replaced with mg cosφ. Therefore the restoring force is reduced to mg cosφ sinθ and the period of oscillation is increased to T = 2π (L/g cosφ)1/2.

In other words, the motion of the pendulum in its plane of oscillation is the same as if gravity were reduced by the factor cosφ.

To change the plane of oscillation the instructor should push a small rod on the mounting bracket with his/her thumb (as shown in pictures above). Students will see an immediate change in pendulum’s period. To fix the angle of the plane, tighten the thumbscrews that anchor the pendulum mounting bracket to the degree plate.

Note: Position of the bob on the rod can be adjusted.