Question

We have an analogy between circular motion and SHM that we can use to describe SHM mathematically. But in order to ensure that black cylinder rotates with exactly the right angular velocity \omegaω so that its motion syncs up with the side to side motion of the glider, there must be some relationship between \omegaω and the properties of the glider/spring system. The goal of this section is to find the fundamental relationship.

1.Draw a force diagram for the glider attached to the spring at any point in its motion. Then write down Newton's second law for the glider. Keep it in a general algebraic form.

2. Substitute the expressions for x(t) and a(t) that you found in the previous sections into the Newton’s second law equation you came up with above. Then simplify the equation to come up with an expression for \omegaω that is necessary for the equation to be true. Record all your work in the text box below.

Answer 1