University of Florida/Egm4313/f13-team9-R1
Problem 1.1 (Pb-10.1 in sec.10.)
[edit | edit source]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 | edit source]Soultion
[edit | edit source]Step 1
[edit | edit source]Step 2
[edit | edit source]Step 3
[edit | edit source]Problem 1.2 (Sec. 1, Pb 1-2)
[edit | edit source]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 | edit source]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 | edit source]Part (a): Determining torque in a hollow cylinder:
[edit | edit source]Part (b): Determining the maximum shearing stress in a solid cylinder:
[edit | edit source]Problem 1.3
[edit | edit source]Problem Statement
[edit | edit source]Given
[edit | edit source]Solution
[edit | edit source]Step One:
[edit | edit source]Problem 1.4 ( Sec. 2, Pb 2-1)
[edit | edit source]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 | edit source]Given
[edit | edit source]Solution
[edit | edit source]Step One:
[edit | edit source]Step Two:
[edit | edit source]Step Three:
[edit | edit source]Problem 1.5 ( P 2.2.5, P 2.2.12, Kreyszig, 2011)
[edit | edit source]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 | edit source]Problem Statement
[edit | edit source]Solution
[edit | edit source]Part (a):
[edit | edit source]Part (b):
[edit | edit source]Problem 2.2.12
[edit | edit source]Problem Statement
[edit | edit source]Solve the initial value problem and graph the solution over the intervals
(1)
Given
[edit | edit source]
Solution
[edit | edit source]Step 1: Find a General Solution
[edit | edit source]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 | edit source]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 | edit source]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 | edit source]Problem 1.6 (P3.17, Beer2012)
[edit | edit source]On our honor, we did this problem on our own, without looking at the solutions in previous semesters or other online solutions.