Chapter 7, Problem 35P

A mechanical system along with its free body diagram is shown in fig. P7.35, where $f=50\text{N}$ is the applied force. The linear displacements $X_1\left(s\right)$ and $X_2\left(s\right)$ of the two springs in the s-domain satisfy the following system of equations:

$40X_1\left(s\right)-40X_2\left(s\right)=\frac{50}{s}$ $(7.144)$ $40X_1\left(s\right)+\left(s^2+65\right)X_2\left(s\right)=0$ . $(7.145)$ (a) Write the system of equations $(7.144)$ and $(7.145)$ 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.