Express the solution of IVP of the function in terms of a convolution integral
Given diff eq is
Take laplace of above diff eq
Take inverse laplce
Express the solution of IVP of the function in terms of a convolution integral
Express the solution of the initial value problem in terms of a convolution integral. (Do not evaluate the integral. There will be an integral in your answer.) y" + 4y = g(t) y(0) = 1, y'(0) = 2
the and Convolution to find Use Laplace transformt solution to the + % IVP y" 24'+ 5y = s y lozo, y/o = -2
6 Express the following function in ut0 10 7. Express the following in terms of r(). 20 0 &. Express the current pulse in the Fig. below in terms of the unit step. Find its integral and sketch it -10
Use
DUHAMEL INTEGRAL / CONVOLUTION INTEGRAL to solve. DO NOT USE
FOURIER SERIES.
Problem 4- Consider a simple damped mass-spring system under a general forcing function p(t) such that: Find the solution x(t) for the periodic forcing function described below: p(t) = Fo [1-cos (? t/2to)1 for 0-t-to (0)-0 for to
Express the area of the shaded region in terms of (a) an integral with respect to x and (b) an integral with respect to y. You do not need to evaluate the integrals. lyx Q y = x Express the shaded region as an integral with respect to X. A= 0 Express the shaded region as an integral with respect to y. A= Sody
Express the area of the shaded region in terms of (a) an integral with respect to x and (b) an integral with respect to y. You do not need to evaluate the integrals. (y=x8 y = / Express the shaded region as an integral with respect to x. A= dx 0 Express the shaded region as an integral with respect to y. A= dy
Express the area of the shaded region in terms of (a) an integral with respect to x and (b) an integral with respect to y. You do not need to evaluate the integrals. Q ya LY Express the shaded region as an integral with respect to x. A= C) ax 0 Express the shaded region as an integral with respect to y A= Soa
Please show work, thanks.
(2) Express the solution of the given initial-value problem in terms of an integral-defined function. 3,94 + (6 cosa)y=f, y0)=1
USE LAPLACE TRANSFORM
Problem 3 Find v.lt) a) Using convolution integral b) Using transfer function c) when us = u(t) +
Solution steps plz
5. Use Duhamel's formula to express the solution of the {x"-7x'+12x = f(t) generic IVP in integral form. 1*(0) = x'(O)=0