Try it! - Transient Analysis

Problem

Given is the following single degree of freedom system with $//<![CDATA[ \begin{array}{l}m=1 \text{kg},\ c=0.1 \frac{\text{Ns}}{\text{m}},\ k=12 \frac{\text{N}}{\text{m}}\end{array} //]]>$, which is not subjected to any external load.

Consider the initial conditions $//<![CDATA[ \begin{array}{l}u_0=1 \text{m},\ v_0=0 \frac{\text{m}}{\text{s}}\end{array} //]]>$.

• Compute the system response using the Newmark-$\beta$ and central difference methods.

• Compare your results with the analytic eigenfrequency of the system.

• Try modifying your time step $//<![CDATA[ \begin{array}{l}\Delta t\end{array} //]]>$. What can you observe for very large values of $//<![CDATA[ \begin{array}{l}\Delta t\end{array} //]]>$?