{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

test2_spring_05

# test2_spring_05 - Name Answers MA-366 Spring 2005 Test 2...

This preview shows pages 1–3. Sign up to view the full content.

MA-366, Spring 2005, Test 2 Name: Answers Note: You may use scratch paper. Show your work. Calculators are not allowed. Problem 1. (12 points) Solve the differential equations: (a) y 00 y 0 C y D 0 Answer: y D e t = 2 C 1 cos p 3 2 t C C 2 sin p 3 2 t (b) y 00 C 10y 0 C 25y D 0 Answer: y D e 5t (C 1 C C 2 t) (c) y 00 C 10y 0 C 24y D 0 , y(0) D 1 , y 0 (0) D 0 . Answer: y D 2e 6t 3e 4t 1

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

View Full Document
MA-366, Spring 2005, Test 2 2 Problem 2. (12 points) A spring-mass system is governed by the equation y 00 C 0.4y 0 C 1.04y D 0. The system is displaced C 5 units from it equilibrium position and set in motion with initial velocity C 4 units/sec. (a) Find the solution y(t) ; Answer: The initial conditions are y(0) D 5 , y 0 (0) D 4 . The solution is y D 5e t = 5 ( cos t C sin t) . (b) Write the solution in the form y D Ae ct cos ( ! t ) . The following formula might be useful: cos (x y) D cos x cos y C sin x sin y. Answer: y D 5 p 2e t = 5 cos (t = 4) . (c) Plot the solution as precisely as you can by marking clearly with their values the first and second x -intercept, and the y -intercept.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 4

test2_spring_05 - Name Answers MA-366 Spring 2005 Test 2...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online