20. Spring Theory. One end of a spring with spring constant k = 6.50N /m is connected to a ball of mass m = 5.00kg while the other end is attached to a ceiling. The ball is initially held in place such that the spring is at its natural length of Lo = 7.00m and at an angle of = 125 deg with respect to the vertical. Once the ball is released from rest, the system undergoes damped oscillation. Find the length L of the spring a very long time after the ball was released. Lo, m

20. Spring Theory. One end of a spring with spring constant k = 6.50N /m is connected to a ball of mass m = 5.00kg while the other end is attached to a ceiling. The ball is initially held in place such that the spring is at its natural length of Lo = 7.00m and at an angle of = 125 deg with respect to the vertical. Once the ball is released from rest, the system undergoes damped oscillation. Find the length L of the spring a very long time after the ball was released. Lo, m

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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You have a prototype Slinky with a lump of coal at the end. This forms a damped spring-mass system. Assuming the usual units you may suppose the mass of the coal m=1, k=3, and the damping constant b = 1. Write down an ODE that models the behavior of this system. If you stretch the spring 1 meter and let it go with no initial velocity, determine the position of the mass after t seconds. At t=4 seconds you whack the mass with a giant candy cane imparting 5 units of impulse. Keeping the same system and the same initial conditions, now determine the position of the mass aftert seconds. PLEASE ANSWER THE LAST QUESTION. (At t=4 seconds you whack the mass with a giant candy cane imparting 5 units of impulse. Keeping the same system and the same initial conditions, now determine the position of the mass after t seconds.)
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Consider the double mass/double spring system shown below. - click to expand. Both springs have spring constants k, and both masses have mass m; each spring is subject to a damping force of F friction We can write the resulting system of second-order DEs as a first-order system, w'(t) = Aw(t), with w = (x₁, x₁, x₂, x₂) T For values of k = 4, m = 1 and c = 21,2 = 0.5±3.2i, V₁ 23,4= - 0.5 ± 1.13i, V3 1, the resulting eigenvalues and eigenvectors of A are -0.039 0.248i 0.813 0.024 +0.153i -0.502 -0.134-0.302i' 0.409 -0.216 - 0.489i 0.661 and (a) Find a set of initial displacements x₁(0), x₂(0) that will lead to the fast mode of oscillation for this sytem. Assume that the initial velocities wil be zero. (x₁(0), x₂(0)) Enter your answer using angle braces, (and ). cx (friction proportional to velocity). (b) At what frequency will the masses be oscillating in this mode? Frequency = rad/s