C solve the initial value problem given by 1 and

• Notes
• 12

This preview shows pages 3–12. Sign up to view the full content.

(c) Solve the initial value problem given by (1) and initial conditions y (0) = 0, y 0 (0) = 0.

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

EGR 265-6D, Fall 2009, Final Exam 4 Problem 4 (12 points) A mass of 10 kg stretches a spring by 50 cm. Include the correct units in all your answers below. (a) Find the spring constant k , assuming that g = 10 m/s 2 . (b) What is the frequency at which the mass oscillates? (c) Find the equation of motion of the mass if it is released from rest at a position 20 cm below the equilibrium position (choose the positive x -axis to be oriented downward). (d) Find the first positive time at which the mass passes through the equilibrium position.
EGR 265-6D, Fall 2009, Final Exam 5 Problem 5 (10 points) (a) Find the gradient of f ( x, y ) = p x 2 + y 3 . (b) Evaluate the directional derivative of f ( x, y ) at the point P (1 , 2) in the direction from P to the point Q (3 , 3). (c) Find a unit vector in the direction of steepest decrease of f ( x, y ) at the point (1 , 2). Also find the rate of increase in this direction.

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

EGR 265-6D, Fall 2009, Final Exam 6 Problem 6 (8 points) Determine parametric equations of the normal line to the graph of z = x x + y at the point (1 , - 2 , - 1).
EGR 265-6D, Fall 2009, Final Exam 7 Problem 7 (8 points) Find the line integral Z C x 2 y ds, where C is a quarter of a unit circle centered at the origin and contained in the first quadrant, starting at (1 , 0) and ending at (0 , 1).

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

EGR 265-6D, Fall 2009, Final Exam 8 Problem 8 (12 points) (a) Show that the force field F ( x, y ) = (4 e y - 2 ye x ) i +(4 xe y - 2 e x ) j is conservative and find a potential function φ ( x, y ) for it. (b) Find the work done by the force field F from part (a) along the curve x ( t ) = t 2 , y = t 3 , 0 t 1.
EGR 265-6D, Fall 2009, Final Exam 9 Problem 9 (10 points) A lamina of constant density ρ ( x, y ) = 1 is bounded by the curves y = x 2 and y = 1. (a) Find the lamina’s mass. (b) Find the lamina’s centroid. Use geometric considerations to simplify your work.

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

EGR 265-6D, Fall 2009, Final Exam 10 Problem 10 (10 points) Find the double integral of the function f ( x, y ) = e x 2 + y 2 over the region in the first quadrant which is bounded by the circles r = 1 and r = 2.
Scratch Paper 11

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

Scratch Paper 12
This is the end of the preview. Sign up to access the rest of the document.
• Fall '10
• Chernov
• Math, EGR, 10 kg, 1 gram

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern