10.3. Simple Pendulum http://www.ck12.org
10.3 Simple Pendulum
Objectives
The student will:
- Understand a simple pendulum.
- Solve problems involving a simple pendulum.
Vocabulary
- simple pendulum:Constructed by attaching any object to one end of a string and attaching the other end of
the string to a fixed point, allowing them to swing back and forth.
Introduction
Asimple pendulumconsists of any object (called a pendulum bob), and a length of string. The dimensions of the
bob are small compared to the length of string. The pendulum is constructed by attaching the bob to one end of the
string and attaching the other end of the string to a fixed point. The bob and string can now swing back and forth.
The effective length of the string is measured from the point at which the string is fixed to the center of mass of the
bob (seeFigure10.9).
FIGURE 10.9
The simple pendulum.Does a simple pendulum perform simple harmonic motion (SHM)? It does, as long as certain assumptions are met.
The string cannot stretch or twist, and the angle of swinging cannot be too great. If the bob moves through as wide
an angle as shown inFigure10.9, then the condition that the restoring force be proportional to the displacement
is not well obeyed (consider the Figure10.10). The component of the bob’s weight,Fxis responsible for the
back and forth motion of the pendulum and acts as the restoring force, which tries to bring the pendulum back to it
equilibrium position at the bottom of its swing. But as we can see inFigure10.10, the restoring force is not parallel