Question

Calculate m. More details in the next post.

Answer 1

What a problem.

The most important thing to realize is that the force from the spring on the left, and the force from the string with the weight on the right, must be equal.

If they were not equal, there would be a net torque on the beam and it would start to rotate.

Now, given that, you can find what the force of the spring is, as it must be equal to the tension in the string.

Then you ask yourself this: that spring force must be equal to half the weight of the beam and weight m. Given that, you can solve for m.