Recent content by ganondorf29

Homework Statement f(t) is given as: from 0 to 0.2s, f(t) = 5 from 0.2s to 0.6s, f(t) = 0 from 0.6s to 0.8s, f(t) = 5, etcHomework Equations for an odd function a0 = 2/p * integral(from -p/2 to p/2) of f(t) dt bn = 4/p * integral(from 0 to p/2) of f(t)*sin(2*pi*n*t/p) dtThe Attempt at a...

Homework Statement x'' + 2\zeta \omega_{n} x' + \omega_{n}^2 x = u_{s}(t) zeta is underdamped and u_{s}(t) is the unit step function and \omega_n is the natural frequency and there are zero initial conditions. Find the total response via the convolution integral. Homework...

For A-5I x1 = x3 x2 = x3 so [1;1;1] is the eigenvector for \lambda = 5 [2,1,2;2,1,2;2,1,2] * [1;1;1] = [5;5;5] But I'm still not sure how to find the eigenvectors for A-0I

Homework Statement A = [2,1,2;2,1,2;2,1,2] Find the Eigenvectors of A Homework Equations The Attempt at a Solution First I found the eigenvalues of A det(A - \lambda I) = 0 \lambda = 0,5 __________________________________________ A-5I...

Homework Statement Find the radius of convergence and the interval of convergence for \sum_{n=0}^\infty \frac{x^n}{n3^n} Homework Equations The Attempt at a Solution Ok, so I first applied the ratio test. \lim_{n\rightarrow\infty} | \frac{x^{n+1}}{(n+1)3^(n+1)} / \frac{x^n}{n3^n} |...

Homework Statement \int sin^3(2x) dxHomework Equations sin^2(x) + cos^2(x) = 1 The Attempt at a Solution First I try to get the integral in the form of \intsin^3(u) and I do this by u-substitution. \int sin^3(2x) dx u = 2x du = 2dx dx = du/2 So the new integral looks as such...

Thank you, I got it.

Homework Statement Determine the area of the parallelogram spanned by the vectors < 0, 9, 6 > and < −10, −6, −4 > Homework Equations Area = A X B The cross product of < 0, 9, 6 > and < −10, −6, −4 > = 0i - 60j + 90k The Attempt at a Solution I know the area is the cross...

Homework Statement A helium-neon laser of the type often found in physics laboratories has a beam power of 3.50 mW at a wavelength of 633 nm. The beam is focused by a lens to a circular spot whose effective diameter may be taken to be equal to 2.00 wavelengths. Calculate the intensity of the...

So is it: \sum\fract(-1)^n^+^2 3x^n /{n}

Homework Statement Determine the Taylor Series for f(x) = ln(1-3x) about x = 0Homework Equations ln(1+x) = \sum\fract(-1)^n^+^1 x^n /{n}The Attempt at a Solution ln(1-3x) = ln(1+(-3x)) ln(1+(-3x)) = \sum\fract(-1)^n^+^2 x^3^n /{n} Is that right?

One more thing. To find the interval on convergence, I know I have to take the ratio test as n-->infinity. Is this how I'm supposed to set it up? lim [x^(n+1) * 5^(n+1) / (n+1)*(n+1)] * [(n*n/x^n*5^x)] n->inf After canceling out some factors I got: lim 1/(2n+1) =...

Is it just Σ(5^n)*(x^n)*10 ?

Homework Statement Determine the series of the given function: f(x) = 10 / (1-5*x) Homework Equations Power series of 1/(1-x) = Σ from n=0 to n=infinity of (x^n) The Attempt at a Solution f(x) = 10/(1-5x) = 10*(1/1-5x) = 10 * Σ(5x)^n = 10 * Σ(5^n)*(x^n) = Σ (50^n)*(x^n) <--- Not sure if...

Homework Statement A particle of charge q = e moves in a circle of radius = 0.44 m with speed v = 2.350×107 m/s. Treating the circular path as a current loop with constant current equal to its average current, find the maximum torque exerted on the loop by a uniform magnetic field of magnitude...