# Free Vibrations - Simple Harmonic Motion

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.

• Its better posted in the Physics SE as it is a physics question, not mathematical – Mathias711 Apr 30 '14 at 10:54
• Do you know how to write equations of motion of this system? – nonlinearism Apr 30 '14 at 17:18

Remember that $f=\omega_n/2\pi$.