University of Florida/Egm4313/f13-team9-R1

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Problem 1.1 (Pb-10.1 in sec.10.)[edit]

On our honor, we did this problem on our own, without looking at the solutions in previous semesters or other online solutions.

Problem Statement[edit]

Soultion[edit]

Step 1[edit]

Step 2[edit]

Step 3[edit]

Problem 1.2 (Sec. 1, Pb 1-2)[edit]

On our honor, we did this problem on our own, without looking at the solutions in previous semesters or other online solutions.

Problem Statement[edit]

Derive the equation of motion of the mass-spring-dashpot in Fig. 53 in K2011 p.85 with applied force r(t) on the ball.

Solution[edit]

Part (a): Determining torque in a hollow cylinder:[edit]

Part (b): Determining the maximum shearing stress in a solid cylinder:[edit]

Problem 1.3[edit]

Problem Statement[edit]

Given[edit]

Solution[edit]

Step One:[edit]

Problem 1.4 ( Sec. 2, Pb 2-1)[edit]

On our honor, we did this problem on our own, without looking at the solutions in previous semesters or other online solutions.

Problem Statement[edit]

Given[edit]

Solution[edit]

Step One:[edit]

Step Two:[edit]

Step Three:[edit]

Problem 1.5 ( P 2.2.5, P 2.2.12, Kreyszig, 2011)[edit]

On our honor, we did this problem on our own, without looking at the solutions in previous semesters or other online solutions.

Problem 2.2.5[edit]

Problem Statement[edit]

Solution[edit]

Part (a):[edit]
Part (b):[edit]

Problem 2.2.12[edit]

Problem Statement[edit]

Solve the initial value problem and graph the solution over the intervals

(1)

Given[edit]


Solution[edit]

Step 1: Find a General Solution[edit]

The ODE is a linear, second-order, homogeneous differential equation with constant coefficients. So, the following equation was chosen as a solution.

(2)

The first and second derivatives are as follows:

(3)

(4)

Plugging the solution and its derivatives back into the original ODE, we receive

(5)

and the characteristic equation

(6)

This gives us 2 real solutions from the quadratic formula, and the general solution:

(7)

Step 2: Solve the IVP[edit]

Equation (7) and its derivative

(8)

can be set equal to the initial values given

(9)

(10)

Solving (9) and (10) simultaneously gives us the c-values and the solution to the IVP

(11)

Step 3: Check Answer with Substitution[edit]

Our solution and its first two derivatives can be substituted into the original ODE

(12)

(13)

(14)

(15)

(16)

Which is true.

Step 4: Graph Solution[edit]
Graph over interval [0,1].
Graph over interval [0,5].

Problem 1.6 (P3.17, Beer2012)[edit]

On our honor, we did this problem on our own, without looking at the solutions in previous semesters or other online solutions.

Problem Statement[edit]

Solution[edit]

Step One:[edit]