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

**1. Homework Statement**

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. Homework 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!