3. Derive the mathematical models for $x_1(t)$ and $x_2(t)$ in the 2DOF system shown. Determine the system transfer functions for $m_1 = m_2 = 10$ kg, $c_1 = 20$ Ns/m, $c_2 = 30$ Ns/m, $k_1 = 10$ N/m, and $k_2 = 40$ N/m.
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Let $x_1(t)$ be the displacement of mass $m_1$ and $x_2(t)$ be the displacement of mass $m_2$. For mass $m_1$: The forces acting on $m_1$ are: - Spring force from $k_1$: $-k_1 x_1$ - Damping force from $c_1$: $-c_1 \dot{x}_1$ - Spring force from $k_2$: $k_2 (x_2 Show more…
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