how can i plotting 3d this differantial functions

how can I December the 3D graph of the function in the image in the specified range of constants c

[Torsten]

I don't see where constants c1 and c2 appear in the differential equation.

Maybe you will have to formulate the ODE more generally in terms of k, m and c.

[Mehmet Aktay]

y= dsolve('4*D2y+8*Dy+4*y=0')

after this code we had generally function

this;

C1.*exp(-t) + C2.*t.*exp(-t)

[Torsten]

And you think these are the C1 and C2 mentioned in the exercise ?

[Mehmet Aktay]

I don't think. they already are

[Mehmet Aktay]

will you help or will you talk in vain?

[Rik]

You can find guidelines for posting homework on this forum here. If you have trouble with Matlab basics you may consider doing the Onramp tutorial (which is provided for free by Mathworks). If your main issue is with understanding the underlying concept, you may consider re-reading the material you teacher provided and ask them for further clarification.

[Torsten]

@Mehmet Aktay

I'm just waiting for an answer on what c1 and c2 are. You said you don't think they are the constants within the solution. Now - then tell us what they are.

Answer 1

[Sam Chak]

Hi @Mehmet Aktay

The Mass(m)–Damper(c)–Spring(k) system behaves just like , a critically-damped system where and .

Therefore, the solution, or the displacement of the mass is given by

.

Taking the time derivative of yields the velocity of the mass

.

At , we have

and

.

Since the ranges are given by and , then you can determine the range of the initial condition, and .

Let's check with @Torsten if my interpretation of the problem is correct or not.