University of Florida/Egm4313/f13-team9-R1
Problem 1.1 (Pb-10.1 in sec.10.)
editOn our honor, we did this problem on our own, without looking at the solutions in previous semesters or other online solutions.
Problem Statement
editSoultion
editStep 1
editStep 2
editStep 3
editProblem 1.2 (Sec. 1, Pb 1-2)
editOn our honor, we did this problem on our own, without looking at the solutions in previous semesters or other online solutions.
Problem Statement
editDerive 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
editPart (a): Determining torque in a hollow cylinder:
editPart (b): Determining the maximum shearing stress in a solid cylinder:
editProblem 1.3
editProblem Statement
editGiven
editSolution
editStep One:
editProblem 1.4 ( Sec. 2, Pb 2-1)
editOn our honor, we did this problem on our own, without looking at the solutions in previous semesters or other online solutions.
Problem Statement
editGiven
editSolution
editStep One:
editStep Two:
editStep Three:
editProblem 1.5 ( P 2.2.5, P 2.2.12, Kreyszig, 2011)
editOn 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
editProblem Statement
editSolution
editPart (a):
editPart (b):
editProblem 2.2.12
editProblem Statement
editSolve the initial value problem and graph the solution over the intervals
(1)
Given
edit
Solution
editStep 1: Find a General Solution
editThe 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
editEquation (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
editOur 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
editProblem 1.6 (P3.17, Beer2012)
editOn our honor, we did this problem on our own, without looking at the solutions in previous semesters or other online solutions.