Question
In: Physics
Sketch a simple pendulum displaced at a small angle. Draw and label all forces acting on...
Sketch a simple pendulum displaced at a small angle. Draw and label all forces acting on the mass. Resolve the component of gravity in the direction of motion. Use Newton's 2nd law to write the dynamic equation that predicts the acceleration of the mass.
Why must the angle be kept small? (Here, it's asking about the experiment with a pendulum that I just did and why the angle had to be kept smaller than 10 degrees)
Solutions
Expert Solution
free body diagram is given below
Simple pendulum's are used to describe simple harmonic motion. If the amplitude becomes large, then the oscillations become chaotic and can no longer be described by simple harmonic motion.
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:
For small angles ?, we can use the approximation
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
and for small angles ? the solution is:
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genius_generous answered 3 hours agoRelated Solutions
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