# Worksheet: The Period of a Pendulum

In this worksheet, we will practice calculating the period and frequency of a pendulum given its length and the local acceleration due to gravity.

**Q1: **

A pendulum has a length of 0.900 m.
What is the frequency of the pendulum? Use a value of
9.81 m/s^{2}
for the local acceleration due to gravity. Give your answer to 3 significant figures.

**Q2: **

A pendulum has a period of 4.81 s. What is the frequency of the pendulum? Give your answer to 3 significant figures.

**Q3: **

A pendulum has a frequency of 4.1 Hz. What is the period of the pendulum? Give your answer to 2 significant figures.

**Q4: **

How long would a pendulum have to be in order to have a period of 10.0 s?
Use a value of 9.81 m/s^{2} for the local
acceleration due to gravity. Give your answer to 3 significant figures.

- A 78.1 m
- B 49.7 m
- C 3.87 m
- D 24.8 m
- E 156 m

**Q5: **

A pendulum has a length of 0.500 m. What is the period of
the pendulum? Use a value of 9.81 m/s^{2}
for the local acceleration due to gravity. Give your answer to 3 significant figures.

- A 0.320 s
- B 0.226 s
- C 1.42 s
- D 0.452 s
- E 27.8 s

**Q6: **

A pendulum with a length of 0.700 m has a mass of
5.50 kg attached to the end of it.
What is the period of the pendulum? Use a value of
9.81 m/s^{2} for the
local acceleration due to gravity. Give your answer to 3 significant figures.

- A 23.5 s
- B 1.68 s
- C 3.94 s
- D 0.716 s
- E 0.839 s

**Q7: **

The acceleration due to gravity on the surface of the Moon is 0.165 times that on the surface of Earth. If a pendulum has a period of 5.60 s when it is on the surface of Earth, what would its period be if it were on the surface of the Moon?

- A 0.924 s
- B 2.27 s
- C 0.440 s
- D 13.8 s
- E 33.9 s

**Q8: **

A pendulum has a period of 3 s. By what factor would the length of the pendulum have to change in order to double its period?

- A4
- B1
- C2
- D
- E

**Q9: **

A pendulum takes 1.42 s to make one complete oscillation. How many complete oscillations does the pendulum make per second? Give your answer to 3 significant figures.

- A
1.42 s
^{−1} - B
0.224 s
^{−1} - C
0.704 s
^{−1} - D
4.42 s
^{−1} - E
1.00 s
^{−1}

**Q10: **

A pendulum has a frequency of 0.23 Hz. By what factor would the length of the pendulum have to change in order to double the frequency?

- A4.0
- B2.0
- C1.4
- D
- E

**Q11: **

A pendulum is taken from Earth to the Moon. Will the pendulum have a higher frequency, a lower frequency, or the same frequency on the surface of the Moon as on the surface of Earth?

- AA lower frequency
- BThe same frequency
- CA higher frequency

**Q12: **

How long would a pendulum have to be in order to have a frequency of
1.50 Hz? Use a value of
9.81 m/s^{2}
for the local acceleration due to gravity. Give your answer to 3 significant figures.

**Q13: **

The figure shows five pendulums hanging from a ceiling. The pendulums have different lengths, and a different mass is attached to the end of each.

Which pendulum has the longest period?

- APendulum
- BPendulum
- CPendulum
- DPendulum
- EPendulum

Which pendulum has the shortest period?

- APendulum
- BPendulum
- CPendulum
- DPendulum
- EPendulum

**Q14: **

A pendulum takes 2.6 seconds to make one complete oscillation. How many times per second does the pendulum move past its equilibrium position? Give your answer to 2 significant figures.

**Q15: **

A pendulum with a length of
20 cm
has a mass of 700 g
attached to the end of it. What is the frequency of the pendulum? Use a value of
9.81 m/s^{2}
for the local acceleration due to gravity.
Give your answer to 2 significant figures.

**Q16: **

The figure shows five pendulums hanging from a ceiling. Each pendulum has a different length, but the same mass is attached to the end of each.

Which pendulum has the longest period?

- APendulum
- BPendulum
- CPendulum
- DPendulum
- EPendulum

Which pendulum has the shortest period?

- APendulum
- BPendulum
- CPendulum
- DPendulum
- EPendulum

**Q17: **

A pendulum makes 1.88 complete oscillations per second. How long does it take the pendulum to complete each oscillation? Give your answer to 3 significant figures.

**Q18: **

The figure shows five pendulums hanging from a ceiling. Each pendulum has a different length and a different mass attached to the end of it.

Which pendulum has the highest frequency?

- APendulum
- BPendulum
- CPendulum
- DPendulum
- EPendulum

Which pendulum has the lowest frequency?

- APendulum
- BPendulum
- CPendulum
- DPendulum
- EPendulum