In: Computer Science
Solve using the same approach as the solution using Matlab for this differential equation d^2y/dt^2 + 6dy/dt + 9y = cos(t) has initial conditions y(0)=1 y'(0)=2, Find Y(s) and without finding y(t), determine what function of time will appear in the solution %} clear, clc syms Y s t real rhs = laplace(cos(t),t,s) eqn1 = s^2*Y - s*2 - 1 + 6*s*Y -1 + 9*Y ==rhs myanss = solve(eqn1,Y) mypart = partfrac(myanss,'FactorMode','real') %{ mypart = (0.08*s + 0.06)/(s^2 + 1.0) + 1.92/(s + 3.0) - 4.3/(s + 3.0)^2 first term yields exp(-b*t)*cos(w*t) 2nd term yields exp(-3*t) 3rd term yields t*exp(-3*t) check %} myanst = (ilaplace(mypart,s,t)) %{ myanst = exp(-t*1.0i)*(0.04 + 0.03i) + exp(t*1.0i)*(0.04 - 0.03i) + 1.92*exp(-3.0*t) - 4.3*t*exp(-3.0*t) %} T = [0, 20] fplot(myanst,T)
`Hey,
Note: Brother if you have any queries related the answer please do comment. I would be very happy to resolve all your queries.
The equation was wrong. I corrected. L{y''(t)}=s^2*y(s)-s*y(0)-y'(0)
clc
clear all
close all
syms Y s t real
rhs = laplace(cos(t),t,s)
eqn1 = s^2*Y - s*1 - 2 + 6*s*Y -6 + 9*Y
==rhs
myanss = solve(eqn1,Y)
mypart = partfrac(myanss,'FactorMode','real')
%{
mypart =
(0.08*s + 0.06)/(s^2 + 1.0) + 1.92/(s + 3.0) - 4.3/(s +
3.0)^2
first term yields
exp(-b*t)*cos(w*t)
2nd term yields exp(-3*t)
3rd term yields t*exp(-3*t)
check
%}
myanst = (ilaplace(mypart,s,t))
%{
myanst =
exp(-t*1.0i)*(0.04 + 0.03i) + exp(t*1.0i)*(0.04 - 0.03i) +
1.92*exp(-3.0*t) - 4.3*t*exp(-3.0*t)
%}
T = [0, 20]
fplot(myanst,T)
Kindly revert for any queries
Thanks.