Video Overview
A pendulum is an object that consists of a mass on the end of a string, wire, or thin rod.
The string, wire, or rod is attached to a surface so that the mass hangs below it.
When the pendulum hangs straight down, it is in its equilibrium position. The weight of the
mass is balanced by the tension in the string. There is no net force acting on the mass at the
end of the pendulum, so it does not move.
When the mass on the end of the pendulum is raised to one side by hand, the weight
of the mass still acts straight downward, but the tension in the string acts diagonally
upward. The tension only partly counterbalances the weight of the mass. This results in a net
force that is perpendicular to the string.
When the pendulum is released, the net force accelerates the mass, and the mass moves closer
to its equilibrium position. However, when the mass reaches its equilibrium position, it has a
sideways velocity, and it overshoots its equilibrium position. The mass moves past the
equilibrium position, and since the string keeps the mass at a fixed distance away from where
the pendulum is attached to the surface, the mass moves upward as well as to the side.
When the mass is on the other side of the equilibrium position, the resultant force due to
the weight of the mass and the tension in the string is in the opposite direction. The mass is
accelerated in the opposite direction, and it moves closer to the equilibrium position again.
The mass will overshoot its equilibrium position again.
The pendulum will keep overshooting its equilibrium position; it will oscillate.
Although the mass of the pendulum determines its weight, it does not affect the period of the
oscillation. For amplitudes less than approximately 1 radian (about
5 7 ∘ 𝑇 𝑙 𝑔 𝑇 = 2 𝜋 𝑙 𝑔 .
Since on the surface of Earth, the acceleration due to gravity is roughly constant, the
main factor that can be used to change the period of the oscillation of a pendulum is its
length.
Consider a pendulum that has a length of
0.5 m . 9.81 m/s2 . 𝑇 = 2 𝜋 0 . 5 9 . 8 1 / 𝑇 = 1 . 4 2 . m m s s ( 3 s . f . )
The amplitude of the oscillation will gradually decrease over time. The kinetic energy of the pendulum
will gradually be lost due to air resistance and due to friction at the point where the pendulum is
attached to the surface above it.
