Theory

A simple pendulum is a device that consists of a weight, called a bob, hanging from the end of a lightweight, inelastic string or rope. When the bob is pulled to the side and released, the pendulum will swing back and forth, exhibiting approximately simple harmonic motion. The period, $T,$ of an object in simple harmonic motion is the time it takes to complete one full oscillation, or cycle. The period of a simple pendulum is a function of its length: $T=2\sqrt[\phantom{2}]{\frac{L}{g}}.$

Procedure

Set the pendulum length to $20cm.$

Release the pendulum from $10$ and record the time it takes for the pendulum to make $10$ oscillations. Repeat this process for $20$ and $30.$

Repeat the previous two steps for lengths of $40cm$ and $60cm.$ You should have three pendulum lengths each with three release angles.

Analysis

Calculate the period for each length$/$release angle combination using $T=\frac{t}{10}$ and then calculate the theoretical period for each length using $T=2\sqrt[\phantom{2}]{\frac{L}{g}}.$

Questions

Why does the period of a simple pendulum remain constant for different release angles despite the pendulum traveling a different distance for each one? Consider the forces acting on the pendulum.

Explain how energy is conserved as a simple pendulum swings. What kind of energy does the pendulum have at the release point, the equilibrium point, and between the two?

How would the results for this experiment differ if it was performed on a planet with a greater acceleration due to gravity than Earth? What about a lower acceleration due to gravity?

Why do you think pendulums are used in clocks?

What were your sources of error in this experiment?

$\backslash$table$[[l,$argle,time $(5)],[20cm,10,8\mathrm{.}51],[20cm,20,8\mathrm{.}55],[20cm,30,8\mathrm{.}48],[,,],[40cm,10,12\mathrm{.}51],[40cm,20,12\mathrm{.}43],[40cm,30,12\mathrm{.}71],[60cm,10,15\mathrm{.}33],[60cm,20,15\mathrm{.}40],[60cm,30,15\mathrm{.}67]]$