E3. Suppose a mass-spring system is described by the ODE u"+9u = 0 with initial conditions u(0) = -1, and u' (0)I= 0. a) How high up and how far down does the mass go? b) What is the velocity of the mass when it passes through equilibrium? c) Will the mass move slower as it passes through equilibrium the 5th time it passes through compared to the 1st time? d) Show that the time between a high point and the subsequent low point is 1/2 the period. e) Show that the time between a high point and the subsequent passage through equilibrium is 1/4 the period. (You might need the identity: arctan(r) + arctan(1/z) = /2.)

E3. Suppose a mass-spring system is described by the ODE u"+9u = 0 with initial conditions u(0) = -1, and u' (0)I= 0. a) How high up and how far down does the mass go? b) What is the velocity of the mass when it passes through equilibrium? c) Will the mass move slower as it passes through equilibrium the 5th time it passes through compared to the 1st time? d) Show that the time between a high point and the subsequent low point is 1/2 the period. e) Show that the time between a high point and the subsequent passage through equilibrium is 1/4 the period. (You might need the identity: arctan(r) + arctan(1/z) = /2.)

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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