This large pendulum demonstrates simple harmonic oscillations. Two bobs of different mass can be set with varying length and can be oscillated in concurrence with a mass rolling along a circular track underneath the pendulum oscillation. The audience will compare modes of oscillations and see how the frequency of oscillations depends on length and mass of the pendulum.

Materials:

• Pendulum Apparatus
• Heavy Bob on String
• Light Bob on String
• A rolling bob

Demo:

To demonstrate the oscillatory motion, simply attach one of the bobs to the dowel rod at the top of the apparatus. Raise the bob to some angle θ where the string is taut and release it. The bob should swing in simple harmonic motion for some time, t.

Explanation:

Simple pendulums are good representations of oscillatory motion. When the bob (mass m)  is displaced by an angle θ from the rest position, it gains gravitational potential energy due to the downward force of gravity, mg (Shown in Fig1). Due to Newton’s Third Law of Motion -for every action there is an equal and opposite reaction- there is an opposite tension force, T acting upwards at an angle θ, or parallel with the string, L (see Fig 1). Since each force acts on the bob at an angle θ, there is a resultant force given by mgsinθ which in mechanics is known as the restoring force (shown by the blue arrow in Fig 1).The restoring force always acts perpendicular to T, and always points towards the equilibrium position, θ = 0.

Figure 1. Showing the forces acting on a bob of mass, m. Tension force acts upwards in red, while the two components of the weight force, mg, are shown in red and blue acting down and towards θ = 0. WebAssign

When the bob is displaced from equilibrium or θ = 0, the restoring force acts on it to bring it back to θ = 0, this is when the acceleration of the bob (a) is maximized. When it reaches θ = 0 the velocity of the bob is maximized and the acceleration is 0. The bob will then swing to –θ and will experience another restoring force towards the θ = 0. The bob will thus swing back in forth in simple harmonic motion.

Over time, the amplitude A will decrease since this simple pendulum does not have perfect simple harmonic motion due to the friction and air resistance removing energy from the system.

Notes:

• When carrying the apparatus, it is much easier to remove the dowel and wind up the string of the bob and carry the base and dowel separately. Do not try and carry as one object.

Written by Phoenix Gallagher