Simple Pendulum
Simple Pendulum
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:
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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
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compared to
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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