Homework Statement
Laplace transform from f(x) = x cos(ax)
to ^f(s) = (s^2 - a^2) / (s^2 + a^2)^2
how do you get the -a^2 term in the numerator,
all i come up with is s^2?
Homework Equations
f(x) = x e^(ax) ----> ^f(s) = 1/(s-a)^2
2 cos(ax) = e^(aix) + e^(-aix)
The Attempt...
Criminal offenses in math textbooks:
#2 Useless diagrams.
Refer to fig 1.a on page#<somepagefaraway>,
fig 1.a (a right triangle with the right angle <ABC labeled 90 degrees)
what is the sin of angle <ABC?
Just say what is sin(90) !
When they make you do problems according to the diagram *they*...
If you calculate for each link on the chain, you will get the same equality.
Now let's assume that the link is horizontally placed, so that mgh is the same for each link.
It appears that the potential energy is the same for all links, and it also appears that the later links will hit the ground...
I don't know how you got 14m/s for the velocity instead of 20m/s, but here is the calculation. it looks like a straightforward high school physics problem.
h = 1/2 g t^2 + v0 t
20m = 1/2 10m/s^2 t^2 + 0
t = sqrt( 2h/g )
t = sqrt( 2*20/10) = sqrt(4) = 2
vf= g t
vf= 10m/s^2 * 2 = 20m/s
1/2 m...
Oh because dL/dq always equals d/dt[ dL/dqdot ]!
no matter what the force is, the force is inclusive in dL/dq
since
L = T - V
and
dL/dq = dT/dq - dV/dq ,
where the force, F = -dV/dq
taking the partial derivative of L w/respect to position q takes care of our generalized force F, so we don't...
Hi, do you have a class you took as an undergrad that you really enjoyed?
I'm interested in hearing what people feel were the best classes they've had.
I ask, because my university has a list of required classes I need to fulfill the physics major requirement; but I feel like it's a wasted...
I noticed another thing
if you take the derivative w/t first, you need to note which expression is from Y1 and which is from X1.
Partial derivatives are commutative, but I can't justify changing the parital derivative back into total derivative d/dt.
Since,
d/dt[ (2t)^2 + t^2] = 8t +2t
but...
Homework Statement
http://www.mathpages.com/home/kmath523/kmath523.htm
In trying to arrive at the Lagrange equations of motion, on the above website, I stumbled over a bit that involved reversing the order of differentiation in the equation (4):
d(partial)/d(partial)X1[(dx/dt)] =...