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WOLFRAM|DEMONSTRATIONS PROJECT

Nonlinearized Motion of a Simple Pendulum

​
length of pendulum
3
initial angle (radians)
π
4
initial angular velocity
0
time to watch motion
10.
show approximation
release system
The motion of a simple pendulum is governed by the nonlinear equation
θ''+g/Lsin(θ)=0
, where
g
is the acceleration due to gravity and
L
is the length of the pendulum. This is the equation that this Demonstration models. In contrast, for small
θ
,
sin(θ)≈θ
, which gives the linear equation
θ''+g/Lθ=0
.
This approximate solution can be made visible, so it may be compared to the exact solution and the conditions under which the approximation is valid can be studied.
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