Motion of 2 masses connected by a rod to a pendulum

[Jenny Physics]

Homework Statement

Find the equation of motion for the system of two masses connected by a massless rod hanging from a pendulum swinging from left to right and back. Use Newton's second law in terms of forces (not in terms of torques).

Relevant Equations

x and y forces

I am not sure which other forces I should consider besides those 3. I cannot consider tensions due to the massless rod on the masses since those will not add up to zero.

 

[haruspex]

Homework Statement:: Find the equilibrium of forces condition for the system of two masses connected by a massless rod hanging from a pendulum.
Homework Equations:: x and y equilibrium of forces

View attachment 255197
I am not sure which other forces I should consider besides those 3. I cannot consider tensions due to the massless rod on the masses since those will not add up to zero.

Is the problem statement exactly as given to you?
Did the diagram come with it or is that your own interpretation?
It is hard to see how it could be in equilibrium unless the pendulum is vertical... unless it is a dynamic equilibrium, e.g. with the pendulum describing a cone about the vertical.

 

[Jenny Physics]

Is the problem statement exactly as given to you?
Did the diagram come with it or is that your own interpretation?
It is hard to see how it could be in equilibrium unless the pendulum is vertical... unless it is a dynamic equilibrium, e.g. with the pendulum describing a cone about the vertical.

You are right, this was a misunderstanding. I edited the question.

 

[haruspex]

You are right, this was a misunderstanding. I edited the question.

I assume the upper rod joins the lower rod at its mid point.
In principle, you would use torque there to figure out the equations, but by symmetry you don't need to. Think whether the behaviour of the upper rod depends at all on the length of the lower rod. What difference would it make to that if it were shrunk to zero?

 

[Jenny Physics]

I assume the upper rod joins the lower rod at its mid point.
In principle, you would use torque there to figure out the equations, but by symmetry you don't need to. Think whether the behaviour of the upper rod depends at all on the length of the lower rod. What difference would it make to that if it were shrunk to zero?

It doesn't depend on the length of the lower rod only because of the symmetry. But what if the pendulum were not attached right at the middle of the lower rod? How could I derive the equations without using torques?

 

[haruspex]

It doesn't depend on the length of the lower rod only because of the symmetry. But what if the pendulum were not attached right at the middle of the lower rod? How could I derive the equations without using torques?

It is provably impossible.
Consider the pendulum rod vertical and the other horizontal, all stationary. Forces alone say all is in balance, regardless where the joint is.