Finding the potential energy of a time dependent force

[GhostLoveScore]

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]

May I ask the origin of this question?

 

[GhostLoveScore]

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]

The change in potential energy of the object should be positive if Fdx is positive.

 

[GhostLoveScore]

The change in potential energy of the object should be positive if Fdx is positive.

OK, then why are we calculating force F as F=-∇U (with minus)