A simple pendulum consists of a point mass suspended from a string or rod of negligible mass, allowing it to oscillate freely. It has one resonant frequency and for small amplitudes, its period can be approximated by an equation involving the pendulum's length and the acceleration due to gravity. This expression is reasonably accurate for small angles of oscillation but treating larger amplitudes is more complex and would require considering the rod's mass.
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A simple pendulum consists of a point mass suspended from a string or rod of negligible mass, allowing it to oscillate freely. It has one resonant frequency and for small amplitudes, its period can be approximated by an equation involving the pendulum's length and the acceleration due to gravity. This expression is reasonably accurate for small angles of oscillation but treating larger amplitudes is more complex and would require considering the rod's mass.
A simple pendulum consists of a point mass suspended from a string or rod of negligible mass, allowing it to oscillate freely. It has one resonant frequency and for small amplitudes, its period can be approximated by an equation involving the pendulum's length and the acceleration due to gravity. This expression is reasonably accurate for small angles of oscillation but treating larger amplitudes is more complex and would require considering the rod's mass.
Copyright:
Attribution Non-Commercial (BY-NC)
Available Formats
Download as DOC, PDF, TXT or read online from Scribd
A simple pendulum consists of a point mass suspended from a string or rod of negligible mass, allowing it to oscillate freely. It has one resonant frequency and for small amplitudes, its period can be approximated by an equation involving the pendulum's length and the acceleration due to gravity. This expression is reasonably accurate for small angles of oscillation but treating larger amplitudes is more complex and would require considering the rod's mass.
Copyright:
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Simple Pendulum
A simple pendulum is one which can be considered to be a point mass suspended from a string or rod of negligible mass. It is a resonant system with a single resonant frequency. For small amplitudes, the period of such a pendulum can be approximated by: Show
For pendulum length
L= g=
cm = m and acceleration of gravity m/s2 the pendulum period is s (Enter data for two of the variables and then click on the active text for the third variable to calculate it.) This expression for period is reasonably accurate for angles of a few degrees, but the treatment of the large amplitude pendulum is much more complex.
If the rod is not of negligible mass, then it must be treated as a physical pend
T=
Pendulum Motion The motion of a simple pendulum is like simple harmonic motion in that the equation for the angular displacement is
Show
which is the same form as the motion of a mass on a spring:
The anglular frequency of the motion is then given by
compared to
for a mass on a spring.
The frequency of the pendulum in Hz is given by
and the period of motion is then
Period of Simple Pendulum
A point mass hanging on a massless string is an idealized example of a simple pendulum. When displaced from its equilibrium point, the restoring force which brings it back to the center is given by:
Show
For small angles , we can use the approximation Show in which case Newton's 2nd law takes the form
Even in this approximate case, the solution of the equation uses calculus and differential equations. The differential equation is
