Simple pendulum subject to a driven force

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SUMMARY

The discussion focuses on the dynamics of a simple pendulum subjected to a driven force, specifically analyzing the forces acting on the pendulum. The equation of motion is derived as -mg*sin(φ) + (-bv) + (Fo*cos(wt)*cos(φ)) = mx'', where Fo represents the driving force, b is the damping coefficient, and g is the acceleration due to gravity. The participants emphasize that the force applied at the suspension point is irrelevant; the critical factor is the pendulum's position over time and its effect on the angle.

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LCSphysicist
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Homework Statement
All below
Relevant Equations
All below
1594327697238.png

The problem is how to construct the right diagram of forces actually

1594327712641.png


Unfortunately, the Fo*cos acting on the ball will not carry the g/l of the solution

-mg*sin(´p) + (-bv) + (Fo*cos(wt)*cos(p)) = mx''
Fo*cos(wt) = mx'' + mg*x/l + bv
 
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LCSphysicist said:
Homework Statement:: All below
Relevant Equations:: All below

View attachment 266128
The problem is how to construct the right diagram of forces actually

View attachment 266129

Unfortunately, the Fo*cos acting on the ball will not carry the g/l of the solution

-mg*sin(´p) + (-bv) + (Fo*cos(wt)*cos(p)) = mx''
Fo*cos(wt) = mx'' + mg*x/l + bv
You do not care what force is applied at the point of suspension. You only care where that point is at time t, and how that affects the angle of the pendulum.
 
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