University of Florida/Egm4313/f13-team9-R1
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
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.