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

#### xinerz

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!

Related Calculus and Beyond Homework Help News on Phys.org

#### StatusX

Homework Helper
Does it satisfy the differential equation and boundary conditions? If so, it's probably right.

#### xinerz

so to find the position at t, i just solve for y in terms of t? like
t = something

also, how would i show if the mass crossed equilibrium at x = 0?

#### StatusX

Homework Helper
No, y(t) is the position at t. And you seem to be using x and y to refer to the same thing. Try graphing the function to see if it crosses 0.

#### Mindscrape

Or just set it equal to zero and see if there is a solution.

#### xinerz

thanks! i got it you guys :)
thanks for all the help!
HAPPY NEW YEAR!