Chapter 7, Problem 36P

Fig. P7.36 shows a system with two-mass elements and two springs. The mass $m_1$ is pulled with a force $f=100\text{N}$, and the displacements $X_1\left(s\right)$ and $X_2\left(s\right)$ of the two masses in the s-domain satisfy the

following system of equations:

$\left(2s^2+50\right)X_1\left(s\right)-50X_2\left(s\right)=\frac{100}{s}$ $(7.146)$ $-50X_1\left(s\right)+\left(2s^2+100\right)X_2\left(s\right)=0$. $(7.147)$ (a) Write the system of equations $(7.146)$ and $(7.147)$ in the matrix form $AX\left(s\right)=b$, where $X\left(s\right)=\left[\frac{X_1\left(s\right)}{X_2\left(s\right)}\right]$.

(b) Find the expressions of $X_1\left(s\right)$ and $X_2\left(s\right)$ using the matrix algebra method.

(c) Find the expressions of $X_1\left(s\right)$ and $X_2\left(s\right)$ using Cramer’s rule.