Question

How do you find the acceleration of a pendulum?

Answer 1

Period of a pendulum:

1. It is the time it takes for a pendulum to travel from its starting pulled-back position across to the other side and back again.
2. This time depends only upon the length $L$., of the pendulum and the acceleration due to the gravity $g$, of the planet, the pendulum is on.

Step 1: Calculate the acceleration of the pendulum

The formula for calculating the acceleration of a pendulum

$\Rightarrow \mathrm{T}=2\mathrm{\pi }\sqrt{\frac{L}{\mathrm{g}}}$

Where, $g$ is the gravitational constant, $L$ is the length, and $T$ is the time.

We can solve the equation for the acceleration due to gravity by first dividing both sides by $2\mathrm{\pi }$which causes this to cancel from the right side,

$\Rightarrow \frac{\mathrm{T}}{2\mathrm{\pi }}=\sqrt{\frac{L}{g}}$

Squaring both sides gives us

$\Rightarrow \frac{{\mathrm{T}}^2}{4{\mathrm{\pi }}^2}=\frac{L}{\mathrm{g}}$

Step 2: Further solve the above terms

Multiply both sides by $g$ to cancel this from the right side,

$\Rightarrow \mathrm{g}\times \frac{{\mathrm{T}}^2}{4{\mathrm{\pi }}^2}=L$

To solve $g$ multiply both sides by the reciprocal of the fraction on the left side, causing it to cancel from the left side,

$\Rightarrow \mathrm{g}=\frac{4{\mathrm{\pi }}^2\mathrm{L}}{{\mathrm{T}}^2}$

Where, $g$ is the gravitational constant, $L$ is the length, and $T$ is the time.

Hence, the above equation is the formula to calculate an acceleration of a pendulum.