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/s2 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/s2 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/s2 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/s2 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 1 4
  • E 1 2

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 1 4
  • E 1 2

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/s2 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 𝐶
  • BPendulum 𝐷
  • CPendulum 𝐸
  • DPendulum 𝐴
  • EPendulum 𝐵

Which pendulum has the shortest period?

  • APendulum 𝐶
  • BPendulum 𝐴
  • CPendulum 𝐵
  • DPendulum 𝐷
  • EPendulum 𝐸

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/s2 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 𝐴
  • BPendulum 𝐸
  • CPendulum 𝐵
  • DPendulum 𝐶
  • EPendulum 𝐷

Which pendulum has the shortest period?

  • APendulum 𝐵
  • BPendulum 𝐴
  • CPendulum 𝐶
  • DPendulum 𝐸
  • EPendulum 𝐷

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 𝐶
  • BPendulum 𝐷
  • CPendulum 𝐵
  • DPendulum 𝐴
  • EPendulum 𝐸

Which pendulum has the lowest frequency?

  • APendulum 𝐷
  • BPendulum 𝐶
  • CPendulum 𝐸
  • DPendulum 𝐴
  • EPendulum 𝐵

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