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 1 . 9 4 × 1 0 8 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 8 . 5 6 × 1 0 6 J
  • B 2 . 0 4 × 1 0 7 J
  • C 8 . 1 5 × 1 0 7 J
  • D 4 . 2 8 × 1 0 6 J
  • E 1 . 7 1 × 1 0 7 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 1 . 5 4 × 1 0 4 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?

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