🎯 Simple Pendulum Experiment

Calculate Acceleration Due to Gravity (g) using Simple Harmonic Motion

✅ FREE Experiment • 📊 Auto Calculations • 🎓 NEB Class 11 Practical

Interactive Simulation

Watch the pendulum swing in real-time. Adjust length and angle to see changes!

Experiment Controls

Range: 50 cm - 150 cm

Range: 5° - 30° (Small angle approximation)

Recommended: 20 oscillations for accurate results

Real-Time Results

Time Period (T)
0.00
seconds
Frequency (f)
0.00
Hz
Gravity (g)
0.00
m/s²
Error
0.00
%

Observation Table

S.No. Length (L)
cm		 No. of Oscillations (n) Total Time (t)
seconds		 Time Period (T)
T = t/n		 T²
sec²		 g
m/s²
No observations yet. Start the experiment and click "Add to Table"

📊 Mean Calculation

Mean value of g = 0.00 m/s²

Standard value = 9.81 m/s²

Percentage error = 0.00%

📚 Theory & Concepts

What is a Simple Pendulum?

A simple pendulum consists of a small bob of mass 'm' suspended from a fixed point by a light inextensible string of length 'L'. When displaced from its equilibrium position and released, it oscillates back and forth under the influence of gravity.

Simple Harmonic Motion (SHM)

For small angles (θ < 10°), the motion of a simple pendulum is approximately simple harmonic. The restoring force is proportional to the displacement, and the motion is periodic.

Time Period Formula

T = 2π√(L/g)

Where:
• T = Time period (time for one complete oscillation)
• L = Length of pendulum (in meters)
• g = Acceleration due to gravity (9.81 m/s²)
• π = 3.14159...

Deriving the Formula for g

From T = 2π√(L/g), we can rearrange to find g:

g = 4π²L/T²

Key Points

🔬 Procedure

  1. Set the initial length of the pendulum (e.g., 100 cm) using the slider
  2. Set a small initial angle (10-15°) to ensure SHM conditions
  3. Choose the number of oscillations (recommended: 20)
  4. Click "Start Experiment" to begin the pendulum motion
  5. The simulation will automatically measure the time for n oscillations
  6. Click "Add to Table" to record the observation
  7. Repeat steps 1-6 for different lengths (e.g., 80, 100, 120 cm)
  8. Click "Calculate g" to compute the mean value of gravity
  9. Compare your result with the standard value (9.81 m/s²)
  10. Calculate the percentage error in your measurement

💬 Viva Questions & Answers

Q1: What is a simple pendulum?
A simple pendulum consists of a small heavy bob suspended from a fixed point by a light inextensible string. When displaced and released, it oscillates about its mean position under the influence of gravity.
Q2: What is meant by time period of a pendulum?
The time period is the time taken by the pendulum to complete one full oscillation (from one extreme position to the other and back). It is measured in seconds.
Q3: Does the time period depend on the mass of the bob?
No, the time period of a simple pendulum is independent of the mass of the bob. It depends only on the length of the string and acceleration due to gravity.
Q4: What is the formula for time period?
T = 2π√(L/g), where T is time period, L is length of pendulum, and g is acceleration due to gravity.
Q5: Why should the angle of displacement be small?
For small angles (less than 10°), the motion is approximately simple harmonic and the time period formula T = 2π√(L/g) is valid. For larger angles, the motion is not purely SHM and the formula becomes less accurate.
Q6: What is the value of g at Earth's surface?
The standard value of acceleration due to gravity at Earth's surface is 9.81 m/s² or approximately 980 cm/s². However, it varies slightly with location.
Q7: Why do we take multiple oscillations instead of one?
Taking time for multiple oscillations (like 20) and then dividing by n reduces the error in measurement. This is because human reaction time error is minimized when measuring a longer duration.
Q8: What are the sources of error in this experiment?
Main sources of error include: (1) Air resistance, (2) Human reaction time in measurement, (3) Amplitude not being small enough, (4) String having mass, (5) Friction at the point of suspension, (6) Inaccurate length measurement.
Q9: What happens to time period if length is doubled?
Since T = 2π√(L/g), if length is doubled (2L), then T becomes 2π√(2L/g) = √2 × T. Therefore, the time period increases by a factor of √2 (approximately 1.41 times).
Q10: Would this pendulum work on the Moon?
Yes, it would work but the time period would be longer because the Moon's gravity is about 1/6th of Earth's gravity (1.62 m/s²). Since T = 2π√(L/g), smaller g means larger T, so the pendulum would swing more slowly.