# Finding the potential energy of a time dependent force

Homework Statement:
Force on an object is F=(m*g/3) *cos(ω*t) in x direction. Find potential energy
Relevant Equations:
U=- ∫(F dx) = - ∫(F*v*dt)
U=-∫F*v*dt= -∫(m*g/3)*cos(ω*t) dt = -(m*g/3 )* (v/ω )* sin(ω*t)

except that according to the official solution, I should be getting positive sign instead of negative. Am I doing something wrong?

hutchphd
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May I ask the origin of this question?

May I ask the origin of this question?

Yes, I have to find a Lagrangian of the pendulum that has a force acting on its top end (which is free to move).

hutchphd