# Worksheet: Forced Oscillations

In this worksheet, we will practice applying simple harmonic motion equations to oscillators driven at various frequencies, including their natural frequency.

Q1:

When divers dive from a 1 m high springboard, before they jump off the board, they bounce on the end of it to increase the height above the pool that they achieve. For a short time, their motion can be modeled as simple harmonic motion.

Consider a diver of mass 55.0 kg who bounces on a springboard with a period of motion of 0.800 s. A second diver bounces on the same springboard with a period of 1.05 s. What is the mass of the second diver?

Q2:

A suspension bridge was found to have an effective force constant of N/m when determining how it oscillates.

How much energy is needed to make the bridge oscillate with an amplitude of 0.210 m?

• A J
• B J
• C J
• D J
• E J

Soldiers march across the bridge and the time between their footfalls is equal to the reciprocal of the bridge’s natural frequency. The soldiers impart J of energy each second. For how long must the soldiers march on the bridge in order to increase the amplitude of the bridge’s oscillations from 0.210 m to 0.500 m?

Q3:

An unloaded diving board oscillates at a frequency of 8.06 Hz. The board has an effective mass of 14.2 kg. What is the frequency of the oscillations of the board if a diver of mass 86.5 kg jumps up and down on it?