University of Florida/Egm4313/f13-team9-R1

Problem 1.1 (Pb-10.1 in sec.10.)

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

Problem Statement

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Soultion

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Step 1

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Step 2

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Step 3

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Problem 1.2 (Sec. 1, Pb 1-2)

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

Problem Statement

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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

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Part (a): Determining torque in a hollow cylinder:

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

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Problem 1.3

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Problem Statement

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Given

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Solution

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Step One:

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Problem 1.4 ( Sec. 2, Pb 2-1)

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

Problem Statement

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Given

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Solution

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Step One:

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Step Two:

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Step Three:

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Problem 1.5 ( P 2.2.5, P 2.2.12, Kreyszig, 2011)

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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

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Problem Statement

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Solution

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Part (a):
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Part (b):
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Problem 2.2.12

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Problem Statement

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

 

(1)

Given

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Solution

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Step 1: Find a General Solution
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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
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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
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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
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Graph over interval [0,1].
 
Graph over interval [0,5].

Problem 1.6 (P3.17, Beer2012)

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

Problem Statement

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Solution

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Step One:

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