- #1
SHISHKABOB
- 541
- 1
Homework Statement
I have the equation mx'' + cx' + kx = 0
where m = 2, c = 12, k = 50, x0 = 0, x'(0) = -8. x is a function of t, and primes denote derivatives w.r.t. t.
Homework Equations
The Attempt at a Solution
so the equation is 2x'' + 12x' + 50x = 0, which I simplify to x'' + 6x' + 25x = 0.
Characteristic equation is r2 + 6r + 25 = 0
using the quadratic formula, I find roots r = -3 ± 4i
therefore the general solution is x(t) = e-3t(c1cos(4t) + c2sin(4t))
I then solve for the unknown constants, c1 and c2:
x(0) = 0 = c1
so x(t) = e-3t(c2sin(4t))
x'(t) = -3e-3t(c2sin(4t) + e-3t(4c2cos(4t))
x'(0) = -8 = 4c2
so c2 = -2
∴ x(t) = e-3t(-2sin(4t))
but... the back of the book gives
x(t) = 2e-3tcos(4t - 3[itex]\pi[/itex]/2)
as the answer...
so I must be doing something horribly wrong, but I have no idea what