Pendulums

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Learn about pendulums and how to calculate period length and the acceleration due to gravity when you have a pendulum

  • A pendulum is composed of a freely swinging mass on a string.
  • The period (T) of a pendulum is the time it takes for one full swing from one side to the other and back.
Pendulum 1

What Effects Period?

The two variables that effect Period (T) is the length of a string (L) and the acceleration due to gravity of that location (g).

On earth we have been using 10 m/s2 but in this unit you may be asked to calculate a specific g of a location.

Pendulum Equation
Pendulum Equation

Pendulum Variables

  • Period (T) with the unit seconds (s)
  • Length (L) with the unit meters (m)
  • Acceleration due to gravity (g) with the unit (m/s2)

Pendulum Period

Pendulum Period is changed by a different length of string (L) or acceleration due to gravity (g)

  • Length of string (L)
Pendulum 1
Short Pendulum
  • Gravity (g)
Pendulum 1
Pendulum at 10 m/s^2
Pendulum on th Moon
Pendulum at 1.6 m/s^2

Pendulum Period is not changed by a different mass or angle if less than 20°

  • Not by mass
Pendulum 1
Pendulum with smaller mass
  • Not by angle of the swing when a small angle less than 20°.  One pendulum in the animation is swinging at 20° while the other is swinging at an angle of 10° with no change to the period.
Pendulum 1
Pendulum at a different angle

1. Which of the following affect the time it takes a pendulum to make one complete swing?

Angle of a swing

Length of a pendulum

Mass of a pendulum

Acceleration due to gravity

Length of a pendulum and acceleration due to gravity

 

Rearranged Pendulum Equation

Observe here how the pendulum equation is rearranged

Pendulum Equation Rearranged

2. What is the period of a 1.0 meter long pendulum on earth composed of a 1 kg mass on a string? (earth g = 10 m/s2)

2

3. What is the period of a 0.5 meter long pendulum on earth composed of a 1 kg mass on a string? (earth g = 10 m/s2)

3

4. What is the period of a 1.0 meter long pendulum on the moon composed of a 1 kg mass on a string? (moon g = 1.6 m/s2)

4

5. What is the acceleration due to gravity on mars where a 1.0 meter long pendulum has a period of 3.256 seconds?

5

Pendulum Problem Set

1. How tall is a tower that has a pendulum hanging down with a period is 24s?

ps1

2. How long should the pendulum be in order to have a period of 1.0 s like in a grandfather clock?

ps2

3. Calculate the length of a cable that supports a pendulum with a period of 3.8 s. 

ps3

4. What is the acceleration due to gravity on a planet where a 1.5 m long pendulum has a period of 3.1 s?

ps4

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