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If I did not know that the coefficient $K$ of the frequency of the pendulum; $\frac{1}{t} = K*(g/L)^{\frac{1}{2}}$ is $\frac{\pi}{2}$, how would I go about finding it? Is there any textbook that I could take a look at? I found some equations through unconventional means with similar structures, but my numbers do not agree with the answers on textbooks. I just need some idea.

Thank you for your time.

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Draw a graph of $\dfrac{1}{t}$ on the $y$-axis and $\sqrt{\dfrac{g}{L}}$ on the $x$-axis.

If the points lie on a straight line passing through the origin, then your experimental value for $K$ is the gradient of the line.

Alternatively draw a graph of $t$ on the $y$-axis and $\sqrt{\dfrac{L}{g}}$ on the $x$-axis to get an estimate of $\dfrac{1}{K}$.

The value of $\dfrac{1}{2 \pi}$ comes from solving the equation associated with simple harmonic motion, which is an approximation to a mass on a simple pendulum with small angles of deflection.

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