13 Jul 2026

Determination of g by a Simple Pendulum

practical ug-vii mechanics simple-pendulum gravity

Aim

To determine the acceleration due to gravity using a simple pendulum.

Apparatus

Small spherical bob, light inextensible string, rigid support, metre scale, stopwatch, and plumb line.

Figure

Simple pendulum arrangement: the length is measured from the point of suspension to the centre of the bob.

Theory

When the bob is displaced through a small angle, gravity has a tangential component that tends to restore it to the equilibrium position. For small angle $\theta$, $\sin\theta\approx\theta$, so the motion is simple harmonic and

\[T=2\pi\sqrt{\frac{l}{g}}.\]

Thus a graph of $T^2$ against $l$ is a straight line of slope $4\pi^2/g$.

Observations

$l$ (m)	Time for 20 oscillations (s)	$T$ (s)	$T^2$ (s$^2$)
0.40	25.4	1.27	1.613
0.60	31.2	1.56	2.434
0.80	36.0	1.80	3.240
1.00	40.2	2.01	4.040

Graph

Observed time period against length for the pendulum.

Result

From the mean period at $l=1.00\,\text{m}$,

\[g=\frac{4\pi^2l}{T^2}=9.79\,\text{m s}^{-2}.\]

Viva Questions

1. Why is the amplitude kept small? To make the small-angle approximation valid.
2. What is the effective length? The distance from suspension point to the bob’s centre.
3. Why time many oscillations? To reduce reaction-time error.

Maxima Code

Download the Maxima calculation file.