Please explain all subparts.I will really upvote S3. Suppose a mass-spring system is described by the ODE y" +9y=0 with initial conditionsy(0) = -1, and y'(0) = 0.a) How far from equilibrium will the mass get?b) Will the mass move slower as it passes through equilibrium the 4th time it passes throughcompared to the 1st time?c) Show that the time between a local max (or min) and the subsequent passage throughequilibrium is 1/4 the period.

Given: Spring-mass system y''+9y=0 Initial condition:y(0)=-1 & y'(0)=0

Answered: S3. Suppose a mass-spring system is…

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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A mass on a spring oscillates according to the equation . When will the mass be halfway to equilibrium for the first time?
QUESTION 3. Consider the mass-spring oscillator without friction: y" + y = 0. Suppose we add a force x(t) which corresponds to a push (to the left) of the mass as it oscillates. We will suppose the push is described by the function x(t) = -u(t – 2n) + u(t – (2n + a)) for some a > 2n which we are allowed to vary. (A small a will correspond to a short duration push and a large a to a long duration push). Here, u(t) is the unit step function. We are interested in solving the initial value problem y" + y = x(t), y(0) = 1, y'(0) = 0.
Please write explanation and don't use the calculator.(Math differential equation) 1. Consider a damped spring-mass system with ? = 1kg, ? = 4 kg/s^2 and ? = 5 kg/s.a. Write the equation of motion (the differential equation) for this systemb. Find the general solution?(?) =c. Solve the initial value problem if ?(0) = 1 and ?′(0) = 0?(?)
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. %3D 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(2) + arctan(1/z) = /2.)
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