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In general, I know that the dynamic equation of pendulum is

theta'' + (k/m)*thata' + (g/l)*sin(theta) = 0

, where k=friction co, m=mass, l=length of string, g=gravity.

But if the pendulum is placed in a constant draft, the equation has to be changed.

Assuming that the pendulum is suspended in a constant horizontal wind,

imparting a constant force w on the bob, the equation is

theta'' + (k/m)*thata' + (g/l)*sin(theta) - (w/m)*cos(theta)= 0

I cannot understand the term of (w/m)*cos(theta). If I rewrite the eq,

m*l*theta'' + (k*l*theta') + (m*g*sin(theta)) - (w*l*cos(theta)) = 0

( inertia )------(friction)--------( gravity )---------( what ?? )

My question is why the length of string, ' l ' affects the external force term.

In my oppinion, external force term is just ( w * cos(theta) ), but the answer is not :(.

Please somebody help me ......

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# Homework Help: Modeling of pendulum with external horizontal force

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