Repeat Problem 9 by using the linearized differential equation of motion, the transfer function, and the state-space form obtained in Problem 8. The parameter values are \(m=0.2 \mathrm{~kg}, M=0.8 \mathrm{~kg}, L=0.6 \mathrm{~m}, k=100 \mathrm{~N} / \mathrm{m}\), and \(g=9.81 \mathrm{~m} / \mathrm{s}^{2}\). The input force \(f\) is the unit-impulse function, which has a magnitude of \(20 \mathrm{~N}\) and a time duration of \(0.01 \mathrm{~s}\).

Data From Problem 9:

Example 5.4 Part

(d) shows how one can represent a linear system in Simulink based on the differential equation of the system. A linear system can also be represented in transfer function or state-space form. The corresponding blocks in Simulink are Transfer FCn and State-Space, respectively. Consider Problem 7 and construct a Simulink block diagram to find the output \(\theta(t)\) of the system, which is represented using

(a) the linearized differential equation of motion,

(b) the transfer function, and

(c) the state-space form obtained in Problem 7. The parameter values are \(M=0.8 \mathrm{~kg}, L=0.6 \mathrm{~m}, k=100 \mathrm{~N} / \mathrm{m}, B=0.4 \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}\), and \(g=9.81 \mathrm{~m} / \mathrm{s}^{2}\). The input force \(f\) is the unit-impulse function, which has a magnitude of \(20 \mathrm{~N}\) and a time duration of \(0.01 \mathrm{~s}\).

Data From Example 5.4:

d. Use Simulink and Simscape to construct block diagrams to find the displacement output x(t) of the system subjected to an applied force f(t) = 10u(t), where u(t) is the unit-step function. The parameter values are m = 1 kg, b = 2 N·s/m, and k = 5 N/m. Assume zero initial conditions.