Tools: stand with a clamp; a thread bar that can be fixed horizontally to the stand; one piece of red string and two pieces of orange thread; two wooden blocks for fixing orange threads between the stand’s clamp; two steel nuts; tape measure, protractor, permanent marker, one staple of $m = 0.0889~{\mathrm g}$.
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5.00
The formula for the oscillation period of a mathematical pendulum is $T=2\pi\sqrt{l/g}$, where $l$ is the length of the pendulum and $g$ is the acceleration due to gravity, valid only for small oscillations. It is known that, in reality, the period $T$ also depends on the angular amplitude $\alpha$, which is the maximum deviation angle of the pendulum from the equilibrium position. For small angles $\alpha < \pi/2$, a good approximation is given by the formula $T=2\pi\sqrt{l/g}(1+A\alpha^2)$, where $\alpha$ is measured in radians and $A$ is a dimensionless constant. Find the value of the constant $A$ experimentally.