Answer Happy

Q3) Consider the translational mechanical system shown. The system consists of a Mass M = 5kg, a damper fo = 5 Ns/m and a spring C = 28 N/m. The input is a force f(t) applied to the mass and x(t) is the output extension = x0 M 0000 С The forces acting on the spring, mass and the damper are Cx(t), *x and for d²x(t) M dx() dt dt? a) Assume zero initial conditions, show that the transfer function is given by 0.2 G(s) where i(s) = G(5)F(5) s? + s + 5.6 (4 Marks) b) Calculate the following: i) The undamped natural frequency. ii) The damping ratio. iii) The steady state gain. iv) The damped natural frequency. v) The peak time. vi) The maximum overshoot. vii) The steady state output to a unit step input using the final value theorem. [7 Marks] c) Produce a sketch of the unit step response step response, ensure the following information is included in your plot and calculated. . The peak overshoots. • Corresponding peak times. Decay rate characteristics. . 19 Ma