{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

G251ex2(fa05)

# G251ex2(fa05) - Math 251 Sections 1/2 November 7 2005...

This preview shows pages 1–4. Sign up to view the full content.

Math 251 – Sections 1/2 November 7, 2005 Second Exam ANSWER KEY There are 9 questions on this exam. Question 1 is worth 20 points. Questions 2 through 9 are worth 10 points each. The total number of points is 100. If a question has multiple parts, then the points assigned to the question are divided equally among the parts, unless otherwise indicated. Where appropriate, show your work to receive credit; partial credit may be given. The use of calculators, books, or notes is not permitted on this exam. Please turn off your cell phone. Time limit 1 hour and 15 minutes.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
1. i. One of the following ODE’s represents the displacement y ( t ) in a spring-mass system with resonance? Circle it. 3 y +108 y = 4 sin 6 t 3 y +108 = 2 sin 6 t 3 y +108 y = 6 cos 3 t 3 y +111 y +108 y = cos 6 t ANS. Frequency of external force and natural frequency match in the last equation. So its the first one. ii For a spring-mass system system with mass equal to 4 kg, spring contant equal to 9 N/m, which damping constant γ causes critical damping? ANS. γ = 4 mk = 6 iii For a spring-mass system system with mass equal to 4 kg, spring contant equal to 9 N/m, damping constant equal to 5, and external force equal to sin t what does the transient part of the solution look like? (Do not determine any constants.) ANS. Since γ 2 - 4 mk is negative the transient part of the solution is a combination of sine and cosine multiplied by a decaying exponential. iv. What is the definition of the Laplace transform of g ( t )? ANS. F ( s ) = 0 e - st f ( t ) dt v What is the following Laplace transform: L{ t 2 e 2 t } ANS. 2 ( s - 2) 3 vi. Circle all the functions among the following that have a Laplace transform : e t 3 t 1 - t | t - 1 | t - 1 e t 1 / 2 ANS. The last two. vii. Suppose that the Laplace transform of y is Y . If y (0) = 2 and y (0) = - 3, then find the Laplace transform of y . ANS. s ( sY - 2) + 3 viii. Suppose that a force of - 3 δ ( t - 1) acts on an object of mass 1 kg. If y (0) = 2 and y (0) = 2, then find y (2).
ANS. y (2) = - 1.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}