Why do we need mathematics

A point mass suspended from an inextensible weightless thread is called a mathematical pendulum. The period of oscillation of a mathematical pendulum is calculated by the formula

T = 2 π \sqrt{\frac{L}{g}}

where $L$ is the length of the pendulum, $g = 9.81 m / s^{2}$ is the acceleration due to gravity and $π = 3.14$ .

Calculate the oscillation period of your pendulum (we denote the calculated oscillation period by $T_{a}$ ). Compare this with the measured results.

The length of my pendulum was:

L =

c m

Comparison of the calculated oscillation period ( $T_{a}$ ) and the measured oscillation period ( $T_{m}$ ) of the pendulum:

T_{a} =

s

T_{m} =

s

Express the formula for the period of oscillation of the pendulum for the length of the pendulum. Using this formula, calculate the length corresponding to the measured oscillation period of the pendulum.

Instructions for calculation

So far we have assumed that we have the length of the pendulum, but the oscillation period of the pendulum needs to be measured or calculated. Now suppose that we have the period of oscillation known from the experiment. Then in the formula for calculating the oscillation period of the pendulum

T = 2 π \sqrt{\frac{L}{g}}

the only unknown quantity is the length of the pendulum, and we can publish it.

Let's first square both sides of the equation, we get

T^{2} = 4 π^{2} \frac{L}{g}

Dividing the equation by $4 π^{2}$ and $g$ , we get

L_{a} = \frac{g T^{2}}{4 π^{2}}

Comparison of the calculated length of the pendulum ( $L_{a}$ ) and the measured length ( $L$ ) :

L_{a} =

c m

L =

c m

How is it possible to measure the length of a string with a stopwatch?