### Solution Found!

# Answer: Derive the system of differential equations describing the straight-line

**Chapter 4, Problem 14**

(choose chapter or problem)

**QUESTION:**

Derive the system of differential equations describing the straight-line vertical motion of the coupled springs shown in equilibrium in FIGURE 4.6.4. Use the Laplace transform to solve the system when \(k_{1}=1, k_{2}=1, k_{3}=1, m_{1}=1, m_{2}=1\) and \(x_{1}(0)=0, x_{1}^{\prime}(0)=-1, x_{2}(0)=0, x_{2}^{\prime}(0)=1 .\)

### Questions & Answers

**QUESTION:**

Derive the system of differential equations describing the straight-line vertical motion of the coupled springs shown in equilibrium in FIGURE 4.6.4. Use the Laplace transform to solve the system when \(k_{1}=1, k_{2}=1, k_{3}=1, m_{1}=1, m_{2}=1\) and \(x_{1}(0)=0, x_{1}^{\prime}(0)=-1, x_{2}(0)=0, x_{2}^{\prime}(0)=1 .\)

**ANSWER:**

Step 1 of 3

The system of differential equation that describes the motion of two masses and in the coupled spring/mass system is

Given,

To solve the system for the initial conditions

For the given values of , the system of differential equations becomes