MA 265 Midterm: ERG_265_-_test_2 Fall 2015
Document Summary
Egr 265, math tools for engineering problem solving. Find the general solution of y + y . 4y = cos x, y(0) = 0, y (0) = 0. A mass of 2 kilograms stretches an undamped spring by 40 centimeters. Assume here that the positive x-direction is oriented downwards. (d) find the rst time t > 0 at which the mass returns to the equilibrium position. Problem 6 (12 points) (a) find the partial derivatives fx and fy of the function f (x, y) = x4y3 + x3 + y2 (b) find the second order partial derivative gxy of g(x, y) = cos(x2 + y2) An undamped sping-mass-system consists of a metal ball of mass m and a spring of sti ness" k. (a) suppose you replace the ball by a heavier ball. Will the system oscillate slower and faster? (b) instead, keeping the same ball, you replace the spring by a sti er spring.
