it has a three different section. everything is included in details about what to do. the main focus is on the arithmetic side of signals and working on Matlab.1. Draw a free-body diagram showing all the forces acting on the mass m shown in Figure 2.
2. From the earlier description, diagrams and the laws of Physics, show that the motion of the system in Figure 2 can be described by the LCCDE (linear constant-coefficient differential equation) below:
3. Using the Laplace transform of the equation above, find an expression for , the system transfer function.
The mass-spring-damper system is a damped second order system. It is common to express the homogenous second order DE for such a damped system as
where is the damping ratio and Wn is the undamped natural (resonant) frequency.
4. From equations (1) and (2), determine expressions for (the damping ratio) and (the natural frequency) in terms of the parameters m, k and C
5. Determine the characteristic equation and eigenvalues (characteristic values) for this system based on equation (2) above.