Problem 3 [25 marks] F k wwwwwww m Figure 3: A spring-mass-damper system. A spring-mass-damper system is portrayed in Figure 3. The external excitation to the system is provided by a slider-crank mechanism and the external force produced is denoted by F. The mass of the object, the spring constant and the damping constant of the system are denoted by m, k and c, respectively. The displacement of the object is denoted by x. Consider the external force F as the input and the displacement x as the output for this system. a) Develop the governing equation of motion for the system shown in Figure 3. [5 Marks] b) Using Laplace transform, develop the governing equation of motion in the com- plex domain. [5 Marks] c) Determine the transfer function of the above system. [5 Marks] d) Recalling that x is the output and F is the input, determine the output Laplace function of the system if m = 10 kg, k = 1 Nm, c=7N-ms and the system is provided with the following force input types: i) Step force input of 10 N. ii) Sinusoidal force input of 10/2sin(10+) N. Hint: sin(a+b)=sin(a) cos(b) + cos(a) sin(b). [5 Marks] [5 Marks]