Consider the spring-mass system with governing ODE and initial conditions below: www m = 1 k = 4 x mx+kx=0 x(0) = 0 x'(0) = 1 a) Very briefly describe in words what the initial conditions mean physically. Find the solution for x(t) ans sketch it. b) Now assume there is a small amount of damping (eg due to air drag) so that the ODE becomes Mx" + cx' + kx = 0 With c = 0.05 and everything else ( parameter and Initial conditions) are unchanged. Sketch the solution of x(t) for this new ODE and explain why it is diff. c) In the following MATLAB code script, complete the bolded lines so that the completed code would use ode45 to numerically solve the ODE from (b) from t = 0 to t = 100 and plot the solution x(t). Hint: First convert the ODE to a system of 1st order ODE's [t,Y]=ode45 (@(t,Y) [ ],.... [ figure(456); clf ploy(t,Y( ], [ ),'b-o'); ]);
Consider the spring-mass system with governing ODE and initial conditions below: www m = 1 k = 4 x mx+kx=0 x(0) = 0 x'(0) = 1 a) Very briefly describe in words what the initial conditions mean physically. Find the solution for x(t) ans sketch it. b) Now assume there is a small amount of damping (eg due to air drag) so that the ODE becomes Mx" + cx' + kx = 0 With c = 0.05 and everything else ( parameter and Initial conditions) are unchanged. Sketch the solution of x(t) for this new ODE and explain why it is diff. c) In the following MATLAB code script, complete the bolded lines so that the completed code would use ode45 to numerically solve the ODE from (b) from t = 0 to t = 100 and plot the solution x(t). Hint: First convert the ODE to a system of 1st order ODE's [t,Y]=ode45 (@(t,Y) [ ],.... [ figure(456); clf ploy(t,Y( ], [ ),'b-o'); ]);
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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please answer the following
![Consider the spring-mass system with governing ODE and initial conditions below:
www
m = 1
k = 4
x
mx+kx=0
x(0) = 0
x'(0) = 1
a) Very briefly describe in words what the initial conditions mean physically. Find the
solution for x(t) ans sketch it.
b) Now assume there is a small amount of damping (eg due to air drag) so that the ODE
becomes
Mx" + cx' + kx = 0
With c = 0.05 and everything else ( parameter and Initial conditions) are unchanged.
Sketch the solution of x(t) for this new ODE and explain why it is diff.
c) In the following MATLAB code script, complete the bolded lines so that the completed
code would use ode45 to numerically solve the ODE from (b) from t = 0 to t = 100 and
plot the solution x(t). Hint: First convert the ODE to a system of 1st order ODE's
[t,Y]=ode45 (@(t,Y) [
],....
[
figure(456); clf
ploy(t,Y(
], [
),'b-o');
]);](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0b248bcb-d422-475d-9311-e6ae6a3d6b31%2F5d647a5d-0e51-46ce-8725-997f21d9e8cc%2Frl8c4c_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the spring-mass system with governing ODE and initial conditions below:
www
m = 1
k = 4
x
mx+kx=0
x(0) = 0
x'(0) = 1
a) Very briefly describe in words what the initial conditions mean physically. Find the
solution for x(t) ans sketch it.
b) Now assume there is a small amount of damping (eg due to air drag) so that the ODE
becomes
Mx" + cx' + kx = 0
With c = 0.05 and everything else ( parameter and Initial conditions) are unchanged.
Sketch the solution of x(t) for this new ODE and explain why it is diff.
c) In the following MATLAB code script, complete the bolded lines so that the completed
code would use ode45 to numerically solve the ODE from (b) from t = 0 to t = 100 and
plot the solution x(t). Hint: First convert the ODE to a system of 1st order ODE's
[t,Y]=ode45 (@(t,Y) [
],....
[
figure(456); clf
ploy(t,Y(
], [
),'b-o');
]);
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