Inverse Laplace Transform

Find the inverse Laplace transform: L-1[(e^-2s)/(s^2)]

Inverse Laplace Transform

Find the inverse laplace transform: L^-1[1/(s^2(s^2+1))]

Inverse Laplace transform

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Inverse Laplace transform

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Solve for y in terms of t

(d^2 * y)/(d * t^2) + 6 * (dy/dt) + 9y = 0 y(0) = 10, y'(0) = 0

Solve for y in terms of t

(d^2 *y)/(d*t^2) + 3*(dy/dt) + 2y = 24* exp(-4*t), y(0)=10, y'(0)=5

Laplace Transform

Find the inverse Laplace transform of (s^3+s^2+2/s) / [s^2(s^2+3s+2)] Using this (or otherwise), Find the solution of the equation y"+3y'+2y = 1-t Find the transform of the following functions: f(t) = (1+t^2)[u(t-1)-u(t-2)] where u(t) is the unit step function. f(t) = sin(t) for 0

Linear system

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Forced harmonic oscillator

Consider the forced harmonic oscillator: y'' + by' + ky = g(t) + y0 where the forcing is made up of two parts, constant forcing (y0) and forcing (g(t)) that changes over time. a) Let w(t) = y(t) - y0/k. Rewrite the forced harmonic oscillator equation in terms of the new variable w. b) In what ways are the solutions of the t ...continues

Solve the differential equation by using convolution

Using convolution, solve this differential equation y"+4y'+13y=(1/3)e^(-2t)sin3t