(adsbygoogle = window.adsbygoogle || []).push({}); Second Order Equations!! Can Anybody help me?? Greatly appreciated!

1. The problem statement, all variables and given/known data

Interpret x(t) as the position of a mass on a spring at time t where x(t) satisfies

x'' + 4x' + 3x = 0.

Suppose the mass is pulled out, stretching the spring one unit from its equilibrium position, and given an initial velocity of +2 units per second.

(A) Find the position of the mass at time t.

(B) Determine whether or not the mass ever crosses the equilibrium position of x = 0.

(C) When (at what time) is the mass furthest from its equilibrium position? Approximately how far from the equilibrium position does it get?

2. Relevant equations

Previous problems on this homework set include transforming the initial value problem into a solution that looks partially like the following:

(example):

y = (1/3)e^(-4t) + (2/3)e^(-4t)

3. The attempt at a solution

I've attempted the following:

x" + 4x' + 3x = 0 --> r^2 + 4r + 3 = 0, solved for r

r = -3 or -1

therefore y=e^(-3t) , y=e^(-t)

y(t) = Ae^(-3t) + Be^(-t)

solved for A and B both = -1/2

however, I'm not sure that this is right.

THANK YOU!

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# Second Order Equations Can Anybody help me? Greatly appreciated!

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