Question

y'' + 16y = (8)(cos(4t)) y(0)=y'(0)= 0

Use Laplace Transforms to solve. Sketch the solution or use matlab to show the graph.

Answer 1

`Hey,

Note: Brother if you have any queries related the answer please do comment. I would be very happy to resolve all your queries.

L{y''+16y}=s^2*y(s)+16*y(s)

s^2*y(s)+16*y(s)=(8*s)/(s^2 + 16)

y(s)=(8*s)/(s^2 + 16)^2

So,

y(t)=t*sin(4*t)

Below is the matlab code to plot

clc% helps in clearing screen
clear all% helps in clearing history
close all% helps in closing files if any
t=0:0.01:2*pi;
y=t.*sin(4*t);
plot(t,y);
grid on;

Kindly revert for any queries

Thanks.