Plotting L–T and L–T² Graphs Using a Simple Pendulum

🎯 Aim

Using a simple pendulum, plot L–T and L–T² graphs. Then use the graphs to find the effective length of a second’s pendulum.

🧰 Apparatus Required

Metallic bob, Vernier calipers, stopwatch, thread, clamp stand, and meter rod.

📘 Theory (Made Simple)

A simple pendulum is just a small heavy bob hanging from a light, inextensible thread.

The time period of the pendulum is given by:

T² = (4π² L) / g

Where:

• L = effective length of the pendulum
• g = acceleration due to gravity

The effective length is:

L = l + h + r

Where:

• l = length of the string
• h = length of the hook
• r = radius of the bob

📷 Original Image Position

A pendulum with a time period of 2 seconds is known as a second’s pendulum.

🧭 Procedure

1. Measure the least count of the Vernier calipers and stopwatch. Note any zero error.
2. Measure the bob’s diameter using the Vernier. Calculate radius: r = d/2. Record hook length h as well.
3. Take a 2-meter thread and mark lengths at 70 cm, 80 cm, 90 cm, 100 cm, etc.
4. Pass the thread through the split cork so the 70 cm mark hangs below.
5. Fix the clamp stand so that the bob is a few centimeters above the floor. Mark the rest position.
6. Displace the bob slightly and release. Record the time for 20 oscillations.
7. Repeat twice more for accuracy.
8. Increase the thread to get an effective length of 80 cm.
9. Repeat the observations.
10. Continue increasing the length to 90, 100, 110 cm, etc., taking readings each time.

📊 Observations

✔️ Precautions

1. Use a stopwatch with a small least count.
2. Thread should be light and inextensible.
3. Support must be rigid.
4. Bob shouldn’t spin while oscillating.
5. Keep amplitude small for accuracy.

⚠️ Sources of Error

1. Suspension point may not be rigid.
2. Amplitude might be too large.
3. Bob may rotate.
4. Human reaction time may affect stopwatch readings.
5. Air currents may disturb the pendulum.