# User:Egm4313.s12.team14.turano

# R2.1[edit]

Given the two roots and the initial conditions:

Find the non-homogeneous L2-ODE-CC in standard form and the solution in terms of the initial conditions and the general excitation

Consider no excitation:

Plot the solution.

Characteristic equation:

Substituting into :

Non-homogeneous solution:

Homogeneous solution:

Overall solution:

No excitation:

From intitial conditions:

Solving for and :

and

So, the final solution is:

# R2.2[edit]

Initial conditions:

No excitation:

Find and plot the solution for

Due to no excitation, becomes:

Substituting into :

Factoring, and solving for :

Since is a double root, the general solution:

From intitial conditions:

Solving for and :

and

So, the final solution is:

# R1.6G[edit]

G) Deformation of a Beam

This equation is of SECOND order and LINEAR.

To prove the applicability of Superposition, the following is done:

Homogeneous

Particular:

Add (Eq. 1) and (Eq. 2):

It could be said that:

and due to the fact that,

It can be said that Y is a solution, confirming that superposition CAN be used. |

# R1.1[edit]

Team14P1R16Diagram1.png

Spring Force,

Dashpot Force,

Applied Force,

From Newton's 2nd Law:

Substituting and into :

Solving for :

Substituting , , and into :

Putting into standard form: