2. (a) A vertical spring, of spring constant k, supports a mass, m. A second spring, of spring constant 2k, connected to the first mass and hanging vertically below it, support a second mass, 3m. Determine the equation of motion of the two masses. [2 marks] (b) Find the frequencies w of the normal modes of vibration of the system described in part (a). [4 marks] (C) An object executes simple harmonic motion with an amplitude 4. (i) (ii) At what values of its position x does its speed equal half its maximum speed? At what values of its position x does its potential energy equal half the total energy? [2 marks] (d) Describe in detail the requirement for a setup of a micro-mechanical experiment that is investigating the coagulation of blood. Sketch what happens on a molecular scale when blood is coagulating. Explain what parameters (e.g. frequency, damping, phase shift, adsorption) the operator has to track to enable measurements that record only viscosity. What precautions have to be taken to minimize unspecific mass uptake during the measurements?