Recent content by TG3

Homework Statement While t<1 , f(t) =0 While t>= 1, f(t) = t^2-2t+2 Find the LaPlace transform of the given function. The attempt at a solution The problem can be re-written as: u1(t)(t^2-2t+2) If it helps, this in turn can be re-written as: u1(t)((t-1)^2+1). I'm not sure it does help...

I don't think so, but I'm not positive... I have trouble focusing for the entire period.

Homework Statement Find the Laplace transform of the given function, a and b are real constants. Hint: cos(bt)=(e^ibt+e^-ibt)/2 and sin(bt)=(e^it-e^ibt)/2i. f(t)=e^(at)*sin(bt) The attempt at a solution The LaPlace transform of e^at is 1/(s-a). The LaPlace transform of sin(bt) is...

When determining a particular solution to a differential equation, one of the necessary steps is to ask the "homogeneous question" aka Does any term in yp solve the homogeneous equation for this problem. When it does, I know that it is necessary to multiple by t. My question is, do I multiply...

The answer given is: .25 cos(8t)

Homework Statement A mass weighing 2 lbs stretches a spring 6 inches. If the mass is then pulled down an additional 3 inches and then released, and there is no damping, determine the position u of the mass at ay time T according to the form Acos(wT-phi). The attempt at a solution The...

Homework Statement Find the general solution for: y''+2y'+5y=3sin2t The attempt at a solution y''+2y'+5y=3sin2t First step is to find the general solution to the homogenous equation, so skipping 2 steps (letting y=e^rt and dividing) R^2+2r+5 (-2+/- sqroot(4-4*5))/2 =-1 +/- 2i...

Homework Statement The half life of carbon 14 is 5730 years long. Assume that dQ/dt = -rQ. Determine the constant rate r. The attempt at a solution dQ/dt = -rQ (Given) dQ/Q = -rdt (algebra) lnQ = -rt (integrate) -lnQ/t = r (algebra) How do I work in...

Homework Statement Find the general solution for y' +3y = t + e^(-2t) for y. The Attempt at a Solution At first I thought that since the equation was already separated, I could simply integrate both sides and get a solution easily: That results in 1.5 y^2 + y = .5t^2 - .5e^(-2t) (Unless I...

Wow, epic fail. Thanks!

Homework Statement Find the plane that contains the line x=3+2T, Y=t, Z=8-t and is parallel to the plane 2x + 4y +8z =17. The attempt at a solution It seemed to me that since the plane is parallel to the plane 2x+4y+8z=17, it must be of the form 2x+4y+8z+D=0 so that it would be parallel...

Homework Statement Find a nonzero vector orthogonal to the plane through points P (0, -2, 0) Q (4, 1, -2) and R (5,3,1) and find the area of the triangle formed by PQR. The attempt at a solution To be honest, I am not entirely sure how to do this problem. I've looked through my textbook...

Homework Statement Show that y = x-(x^-1) is a solution for the differential equations: xy' +y = 2x The attempt at a solution Frankly, I haven't a clue how to start. If it weren't for the x in the xy' term this would be easy, since I could just integrate; unfortunately, I don't know...

Homework Statement Integrate the square root of (x^2 -1) over the interval 0-1. The attempt at a solution First off, I know this is a quarter of a circle, but I'm not supposed to solve it that way. Now then: x = sec theta dx= sec tan theta. square root (x^2-1) dx becomes...

Homework Statement Integrate: (x-1) / (X^2 - 4x +5) The attempt at a solution Normally I would try to factor this into something like (x-1) (x+3) (That's an example completely unrelated to this problem.) However, as no easy factors quickly occurred to me I did a run through of the...