Question 5.19: A Two-Degree-of-Freedom Mass–Spring System Consider the two-...
A Two-Degree-of-Freedom Mass-Spring System
Consider the two-degree-of-freedom mass-spring system shown in Figure 5.106. The mathematical model of the system is given by a set of ordinary differential equations
\begin{gathered} m_{1} \ddot{x}_{1}+\left(k_{1}+k_{2}\right) x_{1}-k_{2} x_{2}=0, \\ m_{2} \ddot{x}_{2}-k_{2} x_{1}+k_{2} x_{2}=0 \end{gathered}
where m_{1}=m_{2}=5 \mathrm{~kg}, k_{1}=2000 \mathrm{~N} / \mathrm{m}, and k_{2}=4000 \mathrm{~N} / \mathrm{m}. Assume that initially \mathbf{x}(0)=\left[\begin{array}{ll}0 & 0\end{array}\right]^{T} and \dot{\mathbf{x}}(0)=\left[\begin{array}{ll}1 & 0\end{array}\right]^{T}.
a. Build a Simulink model of the system based on the mathematical representation and find the displacement outputs x_{1}(t) and x_{2}(t).
b. Convert the ordinary differential equations to the state-space form and repeat Part (a).
c. Build a Simscape model of the physical system and find the displacement outputs x_{1}(t) and x_{2}(t).
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