Characteristic equation: a^2-4a+1=0
Using the quadratic formula gets me a=2+/-sqrt(3)
x=C1e^(2+sqrt3)+C2e^(2-sqrt3)
...
Did I do something wrong?
Um, negative would appear to be correct. Sorry.
So, I dropped the 3 and the 4 and used Euler's formula to turn them into exponentials.
I ended up with
x=ie^((-2-i)t)-ie^((-2+i)t)
Does that mean my roots are -2 +/- i? Or do I have to go further?Edit: Working through, I got
k=5
r=-4
Seems like a legit answer, but was dropping the i...
Homework Statement
x''(t)+r*x't+kx=0
Suppose that for some initial conditions the solution is given by
x=e^(-2t)*(3cos(t)+4sin(t))
What are are and k?
Homework Equations
See aboveThe Attempt at a Solution
I've tried to "brute force" the solution simply by sticking the expression for x...
Yeah, that does make it a bit easier to visualize. In the case of a bullet hitting a metal plate, the medium tends to be denser than the projectile, and all sorts of deformation occurs. In real life this equation would look a bit more like this: http://i.imgur.com/2KA5jiv.gif :p
A...
Ah, I see. So it is meant to be asymptotic? I thought it might be, but it didn't make sense from a physical interpretation, I.E that the bullet never stops moving.
Acceleration becomes more negative, that is, deceleration increases with velocity. So, I could make both terms negative?
Switching the signs in the initial equation only changes whether R is positive or negative. That doesn't solve the fact that my final equation is mathematically impossible.
Homework Statement
A bullet of mass m strikes an amor plate with initial velocity v0. As the bullet burrows into the plate, its motion is impeded by a frictional force which is directly proportional to the bullet's velocity. There are no other forces acting on the bullet.
-Use Newton's Second...