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Pendulum Time Period Change Calculator

Pendulum Time Period Change Calculator

Pendulum Time Period Change Calculator

Calculate the new time period of a simple pendulum due to thermal expansion.

* Ensure consistent units: L₀ in meters, g in m/s², ΔT in Kelvin (or °C), and α in 1/K.

Step 1: Enter Parameters

e.g., 1 m

e.g., 1.2×10⁻⁵ 1/K (typical for steel)

e.g., 50 K (or °C)

Default is 9.81 m/s²

Time period of a simple pendulum: $$ T = 2\pi \sqrt{\frac{L}{g}} $$
With thermal expansion, the new length is: $$ L = L_0 \left(1 + \alpha\, \Delta T\right) $$
Therefore, the new time period is: $$ T’ = 2\pi \sqrt{\frac{L_0\left(1+\alpha\,\Delta T\right)}{g}} $$
Change in time period: \( \Delta T_{pend} = T’ – T_0 \)

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