What is the period of this
pendulum?
T = 2.3 s
14.11 - Interactive problem: a pendulum
On the right is a simulation of a simple pendulum: a bob at the end of a string. You
can control the length of the string, and in doing so change the period of the
pendulum. Your goal is to set the length so that the period is 2.20 seconds. As the
pendulum swings, you will see a graph reflecting the angular displacement of the
bob.
Calculate and set the value for the string length to the nearest 0.05 m using the dial,
then use your mouse to drag the bob to one side and release it to start the
pendulum swinging. There may not be enough room in the window to show the
entire length of the string, but we will show the motion of the bob and the resulting
period. If you do not set the length correctly, press RESET to try again. Refer to the
section on simple pendulums if you do not remember the equation for the period.
You may want to double-check your work by creating an actual pendulum with a
string of the correct length. You can time it: Ten cycles of its motion should take
about 22 seconds.
For small angles, the angular displacement of a pendulum approximates simple
harmonic motion and the graph looks sinusoidal. Try smaller and larger angles and observe the graphs. How sinusoidal do they look to you?
(In the simulation, decreasing the string length makes it easier to create large angular displacements.) You can check the box labeled "SHM" to
draw a sinusoidal graph of SHM motion in black underneath your red graph. The black graph shows simple harmonic motion for the amplitude
you choose and the period calculated by the pendulum equation. If the amplitude is small, you might not see the black graph, because the two
graphs match so closely.14.12 - Period of a physical pendulum
Not all pendulums are simple. A physical pendulum is a rigid extended object (not a
point mass) pivoting around a point. In Concept 1, you see a violin acting as a physical
pendulum.
The equation for the period of a physical pendulum is shown in Equation 1. The
distanceh is the distance from the pivot point to the center of mass of the object. As
always, the moment of inertia must be calculated about the pivot point.The example problem shows how to calculate the period of a meter stick used as a
pendulum in the Earth’s gravitational field. The period is 1.6 seconds. With the use of a
meter stick, this is a result you can verify for yourself. If the stick has a hole close to one
end, put an unbent paper clip through the hole (otherwise, pinch the end very loosely
between your fingers), and set the stick swinging. Ten swings should takeapproximately 16 seconds. Physical pendulum
Mass is distributed
Motion approximates SHM(^286) Copyright Kinetic Books Co. 2000-2007 Chapter 14