Time Period of a Simple Pendulum
A pendulum is a body suspended from a fixed point (pivot) so that it can swing freely. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to restoring force due to gravity that will accelerate it back towards the equilibrium.
Time Period (T): Time period of a simple pendulum is defined as the time taken by the pendulum to finish one full oscillation.
One oscillation of a pendulum is one complete cycle of swinging one way and then returning to its original starting position.
Length of the pendulum: It is the distance between the point of suspension to the center of the body.
Materials required:
- An object (body)
- Thread
- Pencil
- Tape
- Stop watch
- Pen and paper
- Scale
Procedure:
- Tape a pencil horizontally to the top of a table. Lay a pencil on its side and use clear tape to firmly fasten it to a tabletop. Leave about ½ inch (1.3 cm) of the pencil hanging over the edge. The pencil will anchor your pendulum and keep it from falling down, so be sure to use enough tape to secure it and keep it from moving around. Test the pencil by flicking it with your finger. It should stick to the table top.
- Tie a loop about 1 inch (2.5 cm) in diameter at one end of the string. Take a length of string 2-3 feet (0.61 – 0.91 m) long and curl one end to form a loop. The loop needs to fit around the pencil, but not too tight or it won’t swing properly. Tie knot with the loop to keep it from coming undone. Slide the loop onto the pencil and slide it off to make sure it’s not too tight.
- Make a small ½ inch (1.3 cm) hook with a metal wire. Take a 2-inch (5.1 cm) length of metal wire and curl one end of it into a “J” shape to form your hook. The hook will hold the weight that swings the pendulum so shape your hook so it’s easy to attach and remove nuts onto it to alter the weight of the pendulum. You can use pliers to curl the metal wire.
- Slide a 1/4-inch (0.64 cm) nut onto the end of the hook. Use a standard metallic nut as the weight for your pendulum. The hole in the center makes a nut ideal for sliding onto the hook, and you can easily add or remove nuts to experiment with different weights.
- Tape a piece of paper on a wall or table behind the hook. You can use the paper to mark where you release the pendulum each time so you can see the way the pendulum behaves and swings based on where you release it. Tape the paper so that it is a backdrop behind the hook with the nut on it. Any colour paper is fine, as long as you can see the pencil markings.
- Record the length of the pendulum.
- Pull the hook with the nut on it back about 5 inches (12.5 cm). Before you release it, use your pencil to mark on the paper taped behind the pendulum where you release it from. That way, you can repeat the experiment by letting the pendulum go from the same place each time. You need to have a consistent release point for accurate results in your experiments!
- Release the pendulum and start a stopwatch. When you release the pendulum, count 10 oscillations and note down the time to complete 10 oscillations.
- Now calculate: Time period = time taken to complete 10 oscillations/10
- Now repeat step 6, 7 and 8 for more 2 times and calculate the average.
- Now increase the length and repeat step 6,7,8 and 9.
Observation:
You will observe that when you increase the length, the time period is also increased.
Result:
Time period of the pendulum depends on length of the pendulum.
When length of the pendulum increases, the time period of the pendulum is also increasing.
When length of the pendulum decreases, the time period of the pendulum is also decreasing.
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