An object of mass 4 grams hanging at the bottom of a spring with a spring constant 5 grams per second square. Denote by y vertical coordinate, positive downwards, and y = 0 is the spring-mass resting position. TI m y(t) y (a) Write the differential equation y" = f(y, y') satisfied by this system. f(x,y) = -5y/4 Note: Write t for t, write y for y(t), and yp for y' (t). (b) Find the mechanical energy E of this system. E(t) = 2((yp))^2+(5/2)y^2 Note: Write t for t, write y for y(t), and yp for y' (t). (c) If the initial position of the object is y(0) = 1 and its initial velocity is y' (0) = -3, find the maximum value of the object velocity, Umax > 0, achieved during its motion. Umax = sqrt(19/2) Σ Σ m Σ

An object of mass 4 grams hanging at the bottom of a spring with a spring constant 5 grams per second square. Denote by y vertical coordinate, positive downwards, and y = 0 is the spring-mass resting position. TI m y(t) y (a) Write the differential equation y" = f(y, y') satisfied by this system. f(x,y) = -5y/4 Note: Write t for t, write y for y(t), and yp for y' (t). (b) Find the mechanical energy E of this system. E(t) = 2((yp))^2+(5/2)y^2 Note: Write t for t, write y for y(t), and yp for y' (t). (c) If the initial position of the object is y(0) = 1 and its initial velocity is y' (0) = -3, find the maximum value of the object velocity, Umax > 0, achieved during its motion. Umax = sqrt(19/2) Σ Σ m Σ

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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