# Resonance of a driven pendulum

The amplitude of an oscillating body becomes maximum when the frequency of the driving force is equal to its natural resonant frequency. A driven pendulum is a very simple example of such a system.

# Objective

Demonstrate the resonance of a driven pendulum. The pendulum is made by two button shaped magnets suspended on a piece of paper. A coil powered from SQ1 provides the driving force.

# Procedure

Make a pendulum using two button magnets and a piece of paper. Suspend it and place the 3000T coil near that, as shown in figure.

- Connect the coil between SQ1 and ground
- Calculate the resonant frequency from the length of the pendulum
- Adjust the frequency around the expected resonance frequency

# Discussion

When SQ1 reaches the resonant frequency of the pendulum, the amplitude goes up due to resonance. A 4 cm (from the center of the magnet to the axis of oscillation) long pendulum resonated at around 2, 5 Hz, almost tallying with its calculated natural frequency. The resonant frequency of the pendulum is given by f= 1 ⁄ (2π√(g⁄l)), where l is the distance from the center of the magnet to the point of suspension and g is the acceleration due to gravity.

Repeat the experiment by changing the length of the pendulum.