| # | $L$ (cm) | $t_{20}$ (s) | $T = t/20$ (s) | $T^2$ (s²) | $L / T^2$ |
|---|---|---|---|---|---|
| No records logged yet. Time 20 swings and log. | |||||
| # | $L$ (cm) | $t_{20}$ (s) | $T = t/20$ (s) | $T^2$ (s²) | $L / T^2$ |
|---|---|---|---|---|---|
| No records logged yet. Time 20 swings and log. | |||||
Principle: A heavy spherical bob suspended by a light, inextensible thread from a rigid support undergoes simple harmonic motion for small angular displacements ($\theta \le 15^\circ$). The restoring torque is proportional to the angular displacement:
Time Period ($T$):
where $L$ is the effective length measured from the point of suspension to the center of gravity of the bob ($L = l + h + r$).
Second's Pendulum: A pendulum whose period of oscillation is exactly $2\text{ seconds}$ (takes $1\text{ s}$ for each swing from one extreme to the other). Its length $L_s$ is given by:
$L\text{–}T^2$ Graph: A plot between effective length $L$ on the x-axis and $T^2$ on the y-axis is a straight line passing through the origin. The acceleration due to gravity is determined from the slope: