Simple pendulum experiment : Aim
To investigate whether the time period of a simple pendulum depends on the mass of the bob while keeping the length constant.
Simple pendulum experiment : Materials required
Light, inextensible string (fixed length, e.g., 50 cm or 100 cm)
Three or four bobs of the same size but different masses (e.g., 40g, 60g,80g,and 100g)
A rigid stand with clamp
A stopwatch or a stop clock
A meter scale
A marker or chalk (to mark the equilibrium position)
Simple pendulum experiment : Formula
Simple pendulum experiment : Theory
A basic pendulum is made up of a small, heavy bob that is free to swing back and forth under the force of gravity. It is suspended from a fixed point by a light, inextensible (non-stretchable) string.
The bob starts to oscillate, or move to and fro, in a regular, periodic way after being released and slightly moved from its rest position.
Key Term : Time Period (T)
The time period is the amount of time it takes the pendulum to swing from one extreme end to the other and back again, or to complete one full oscillation.
where:
L is the pendulum’s effective length, measured from the suspension point to the bob’s center of mass.
g =Acceleration due to gravity
Simple pendulum experiment : Procedure
Set up the pendulum:
Securely fasten one end of the rope to the clamp with a split rubber cork after hanging the bob.
Connect the other end to the metal bob.
Verify that the bob is hanging freely and not touching anything.
Calculate the Effectiveness Length: Determine the distance between the center of the bob and the bottom of the split rubber cork using a meter scale.
Throughout the experiment, keep the pendulum’s length L constant(for example, 50 or 100 cm) and maintain it there.
To permit oscillations, move the bob a little (angle < 10°) and then let go.Calculate the time (t) required for 20 full oscillations using a stopwatch or stop clock.
For every bob, repeat the measurement three times, then average the results.
Measure the time period:
The time period is the amount of time it takes the pendulum bob to complete one oscillation.
Pull the bob out of the vertical position by about 5 to 10 degrees.Release it gently so that it begins oscillating around the mean position without exerting any force.
After a few oscillations are finished, start the stopwatch when it crosses the equilibrium position.
Twenty complete oscillations, or one complete cycle from side to side and back, must be counted.To determine the duration of a single oscillation, divide the total time by 20.
By maintaining a constant length, the experiment is repeated for varying masses.
A graph between the time period and the mass of the data is created using the tabulated readings.
Simple pendulum experiment : Tabular column
| Sl.No. | Mass of
the bob (m) |
Time for 20 oscillations (t)
|
Mean
time (t) |
Time
period (T) T= t /20 |
| (g) | (s) | (s) | (s) |
| Trial 1 | Trial 2 | Trial 3 | ||||
| 1. | 40 | 30 | 29 | 30 | 29.67 | 1.48 |
| 2. | 60 | 30 | 29 | 30 | 29.67 | 1.48 |
| 3. | 80 | 29 | 30 | 30 | 29.67 | 1.48 |
| 4. | 100 | 30 | 30 | 29 | 29.67 | 1.48 |
Simple pendulum experiment : Graphical Representation
Plotting time period (T) against mass (m) would provide a horizontal line, indicating that T is independent of m. The conclusion that changes in the mass of the pendulum bob have no effect on the time period of a simple pendulum would be graphically supported by this graph.
The time period (T) in this graph stays constant at roughly 1.48 seconds for a range of pendulum bob masses (m).
Here is a straightforward numerical depiction of the graph to help you see it better:
Simple pendulum experiment : Result and Interpretation
We can observe from the tabular column that for a variety of masses, the simple pendulum’s time period stays roughly constant. This suggests that the mass of the pendulum bob has no bearing on the time period of a basic pendulum.
Simple pendulum experiment : Conclusion
The above experiment shows that the time period of a basic pendulum is determined solely by the length of the pendulum acceleration due to gravity, not by the mass of the pendulum bob.The theoretical model is validated by this. T = 2π √(L/g) is the theoretical equation.
Simple pendulum experiment : Precautions
To prevent changes in length, use a string that is light and inextensible.
To preserve SHM conditions, make sure the angular displacement is modest (less than 10°).
To reduce the impacts of air resistance, make sure the pendulum bobs are identical in size and form.
To reduce any external vibrations or disruptions, use a sturdy support.
Accurately measure the pendulum’s length and maintain it throughout the experiment.
Measurements should be repeated to reduce human error.
Measure the amount of time it takes for oscillations using a stopwatch or timer that is accurate enough.
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