# 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 $$x_{1}(0)=0, x_{1}^{\prime}(0)=-1, x_{2}(0)=0, x_{2}^{\prime}(0)=1 .$$

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 $$x_{1}(0)=0, x_{1}^{\prime}(0)=-1, x_{2}(0)=0, x_{2}^{\prime}(0)=1 .$$

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

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