In Problem 52, part (b), solve assuming (k_{1}=k_{2}=) (k_{3}=k_{4}=k) and (m_{1}=m_{3}=m) and (m_{2}=m(1+epsilon)). Use the same parameter

Question:

In Problem 52, part (b), solve assuming \(k_{1}=k_{2}=\) \(k_{3}=k_{4}=k\) and \(m_{1}=m_{3}=m\) and \(m_{2}=m(1+\epsilon)\). Use the same parameter values. Discuss.

Problem 52:

(b) For the previous system, suppose that \(k_{1}=k_{3}=\) \(k_{4}=k=1 \mathrm{~N} / \mathrm{m}, m_{1}=m_{2}=m_{3}=m=1 \mathrm{~kg}\), and \(k_{2}=(1+\epsilon) k=(1+0.05) k\), where \(\epsilon\) signifies a stiffness imperfection. Solve for the frequencies and modes of vibration and plot the modes and responses for \(x_{1}(0)=0.5 \mathrm{~cm}\) and all other initial conditions equal zero.

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