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Differential Equations - Systems of Equations, Laplace Transform System of Equations.

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I am looking for help with review problems for my final exam. I narrowed down the problems I am have the most difficulty with and need help with. I need the problems worked out so I can practice the appropriate steps for success on the final next week.

1. A 32 pound weight stretches a spring 2 Feet. The mass is then released from an initial position of 1 foot below the equilibrium position. The surrounding medium offers a damping force of 8 times the instantaneous velocity. Find the equation of motion if the mass is driven by an external force of 2cos5t.

2. Solve the system where X and Y are functions of t:

dx/dt = 4x - y
dy/dt = 2x + y

3. dx/dt + 3x + dy/dt = 1 x(0) = 0
dx/dt ? x + dy/dt - y = e^t y(0) = 0

4. Use Laplace Transforms to solve the system where X and Y are functions of t:

dx/dt ? 5x ? 4y = 0 x(0) = 1

5. Dy/dt + x ? y = 0 y(0) = -1

Solution Summary

The systems of equations and Laplace transform systems of equations are examined.

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1.

A 32 pound weight stretches a spring 2 Feet. The mass is then released from an initial position of 1 foot below the equilibrium position. The surrounding medium offers a damping force of 8 times the instantaneous velocity. Find the equation of motion if the mass is driven by an external force of 2cos5t.

Let x(t) be the distance of the mass from equilibrium.
The force exerted by ...

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