As an engineering enthusiast I have been practicing with numerous model assignments to see how well I could deal with dynamics if I were in an educational environment. Most problems seem simple to solve but I have come accross this question concerning simple harmonic motion.
Please see the link below, the question I am having trouble starting is called part 2 in the model assignment:
http://www.freestudy.co.uk/engineering%20science%20h1/ass2%201.pdf
Please note that I am only interested in completing part A of question 2.
An experiment includes a wheel with a moment of inertia ($I$). A mass ($M$) is connected to a belt and runs over a drum of radius ($R$). The other end of the belt is attached to a spring of stiffness ($K$) that is connected to the ground.
Show that if the mass is pulled down with a force ($F$) and then released, that the system will oscillate with simple harmonic motion with a frequency given by…
$$F = \frac{1}{2\pi} \sqrt{\frac{k}{M+\frac{I}{R^2}}}$$
I would really like to understand how a problem like this could be solved, I have no idea where to even start to be honest.
Read the solution of Problem A-3-12 in this pdf by A. Aziz Bazoune.
Remember that $f=\omega_n/2\pi$.