1. The problem statement, all variables and given/known data I have an extended system consisting of a track, a spring, a spring attached to a moving cart on one end, a string attached to the other end of the cart, and a hanging object attached to the end of the string. I need to find one equation that allows me to measure the total frequency distribution of the system. In my body diagram, I found forces of kx for the force of the spring, the tension of the string on cart in the +x direction and as a force on the hanging object in the +y direction. Finally, a force of mg on the hanging object's wieght. From doing the experiment, the frequency was found by measuring the oscillations of the spring in completing a period as a total time was taken for it to complete its cycle. I'm not sure how to find the final equation for the freqency. 2. Relevant equations Newton second law of motion: Force = mass x acceleration Hooke's law for the force of the spring: F(spring) = -k(constant)x X(displacement of spring) Forces of system: In x direction: T-kx=ma In y direction: T-mg=ma=0, T=mg Total forces of system: mg-kx=ma In measuring angular frequency: ω = √k/m For measuring frequency: f = 1/2∏√k/m For measuring period: T = 2∏√m/k 3. The attempt at a solution The attempts I've made so far are shown above in determining the total forces of the system. I am not sure now how to incorporate the either the angular frequency or frequency of the system as a measure of total forces into one equation. Any help is appreciated! And hope this makes sense, I'm doing all this to put together into my lab report.