Using Effective Potential to Describe motion of an object

[Junkwisch]

Hey guy, this is one of the question in my uni work (I'm not sure whether my answer is correct or not, please have a check). The attachment consists of what the effective potential graph look like.





"It starts from a low point where it move downward to the lowest point. It then move upward to the highest point then to the lowest point parabolically. It then move upward to the low point (where the motion start) and restart the entire process again."



I treat the effective potential as the displacement of the object in Y, since the only potential energy acting in here is gravitational. Omega represent angular velocity, g= acceleration due to gravity and L represents the length if the arm.


Best Regards
Naphat Veraphong

 

[paisiello2]

Can you define all the terms you are using?

 

[Junkwisch]

Two light, inextensible rods OP and PQ are joined at P by means of a frictionless hinge. The
rod OP stands vertically. Its base O is glued to the centre of a rotating turntable. The rod PQ
makes an angle θ(t) with respect to the vertical, which changes as a function of time t, with
0 ≤θ(t) ≤ pi . Both rods rotate around the axis OP with constant angular velocity Ω. A point
mass m is attached to the free end Q of the rod PQ.

L is the length of rod PQ, g is uniform acceleration due to gravity

 

[paisiello2]

What is E and Veff?

 

[Junkwisch]

E is the energy while Veff is effective potential

 

[paisiello2]

Not sure why the mass m and length L terms are missing from the equation for E.

What is the definition of the effective potential?