A metronome is used to keep time in music much like a Grandfather clock keeps time. It uses a pendulum in simple harmonic motion. Like a child on a swing or flying trapeze artist, a metronome can be set at certain frequencies. Use your knowledge of period and frequency to complete these practice problems.
| Problem | Picture | Given/Find | Equation | Solution |
|---|---|---|---|---|
| A metronome is set with a frequency of 180 cycles per minute. What is the period of the metronome? |
|
\(\mathsf{ T = ? \text{ s} }\) \(\mathsf{ f = 180 \text{ } \frac{\text{cycles}}{\text{min}} \times \frac{1 \text{ min}}{60 \text{ sec}} = 3.0 \text{ Hz} }\) |
\(\mathsf{ T = \frac{1}{f} }\) | \(\mathsf{ T = \frac{1}{3.0 \text{ Hz}} = 0.33 \text{ s} }\) |
| A child swings on a swing with a period of 5.0 seconds per back and forth swing. What is the frequency of the swing? |
|
\(\mathsf{ T = 5.0 \text{ s} }\) \(\mathsf{ f = ? \text{ Hz} }\) |
\(\mathsf{ f = \frac{1}{T} }\) | \(\mathsf{ f = \frac{1}{5.0 \text{ s}} = 0.20 \text{ Hz} }\) |
| A 120.0 kg object oscillates on a spring with a period of 2.45 seconds. What is the object's frequency of oscilation? |
|
\(\mathsf{ T = 2.45 \text{ s} }\) \(\mathsf{ f = ? \text{ Hz} }\) |
\(\mathsf{ f = \frac{1}{T} }\) | \(\mathsf{ f = \frac{1}{2.45 \text{ s}} = 0.408 \text{ Hz} }\) |
