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Differential Equations and Springs 1

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Differential Equations and Springs

1. Solve the initial-value problems and graph the solutions on the same set of axes.

y'' + 4y' + 2y = 0 y(0) = 5; y'(0) = 0

y'' + 4y' + 2y = 0 y(0) = 0; y'(0) = 5

2. Repeat problem 1 for the equation:

y'' + 2y' + 5y = 0 y(0) = 5; y'(0) = 0

y'' + 2y' + 5y = 0 y(0) = 0; y'(0) = 5

3. An object having a mass of 1 kg. is suspended from a spring with a spring constant (k) of 24 Newtons/meter. A shock absorber which induces a drag od 11v newtons (v is in meters/second) is included in the system.

The system is set in motion by lowering the bob 25/3 centimeters and then striking it hard enough to impaet an upward velocity of 5 meters/sec; solve for and graph the displacement function.

repeat this exercise (all on the same graph) for cases where the bob is lowered:

12, 20, 30, and 45 centimeters.