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3.2 Mass-spring system (harmonic oscillator) Solve the following IVP using the same instructions from the beginning of the section as you did in the previous problem. A mass m = 1, sliding on a friction-less horizontal surface, is connected to a spring with the spring constant k = 4. Newton's law ma = F, combined with Hooke's law F-ka, where a is the displacement of the mass at time t (and hence can be denoted z(t)), which is the same as the amount by which the spring is stretched or compressed, yields = d²x dt2 -kx The motion is started by displacing the mass from the equilibrium by 1, holding it there, and then at time t= 0 carefully releasing it, so that the initial velocity is 0. In other words, the initial condition is: m- x(0)=1, and (0) = 0. ż

3.2 Mass-spring system (harmonic oscillator) Solve the following IVP using the same instructions from the beginning of the section as you did in the previous problem. A mass m = 1, sliding on a friction-less horizontal surface, is connected to a spring with the spring constant k = 4. Newton's law ma = F, combined with Hooke's law F-ka, where a is the displacement of the mass at time t (and hence can be denoted z(t)), which is the same as the amount by which the spring is stretched or compressed, yields = d²x dt2 -kx The motion is started by displacing the mass from the equilibrium by 1, holding it there, and then at time t= 0 carefully releasing it, so that the initial velocity is 0. In other words, the initial condition is: m- x(0)=1, and (0) = 0. ż

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Differential equation: can anyone here please solve 3.2 par correctly and handwritten 

Which method works on which problem? For each of the problems in this section do the following: 1. State which methods work and which don't and why. (Recall, our methods are: guess and check, integration, ert, separation of variables, and Laplace transform). 2. Solve the given problem by all of the methods that work. 3. Check your answer by plugging into the DE and IC. 4. Plot the graph. Rough sketch is OK. 3.1 Logistic growth Solve the initial value problem (IVP): y' = 10y-y², y(0) = 1, 3.2 Mass-spring system (harmonic oscillator) Solve the following IVP using the same instructions from the beginning of the section as you did in the previous problem. A mass m = 1, sliding on a friction-less horizontal surface, is connected to a spring with the spring constant k = 4. Newton's law ma = F, combined with Hooke's law F = -ka, where a is the displacement of the mass at time t (and hence can be denoted r(t)), which is the same as the amount by which the spring is stretched or compressed, yields d²x dt² m- -kr The motion is started by displacing the mass from the equilibrium by 1, holding it there, and then at time t= 0 carefully releasing it, so that the initial velocity is 0. In other words, the initial condition is: x(0) = =1, and (0) = 0.
Transcribed Image Text:Which method works on which problem? For each of the problems in this section do the following: 1. State which methods work and which don't and why. (Recall, our methods are: guess and check, integration, ert, separation of variables, and Laplace transform). 2. Solve the given problem by all of the methods that work. 3. Check your answer by plugging into the DE and IC. 4. Plot the graph. Rough sketch is OK. 3.1 Logistic growth Solve the initial value problem (IVP): y' = 10y-y², y(0) = 1, 3.2 Mass-spring system (harmonic oscillator) Solve the following IVP using the same instructions from the beginning of the section as you did in the previous problem. A mass m = 1, sliding on a friction-less horizontal surface, is connected to a spring with the spring constant k = 4. Newton's law ma = F, combined with Hooke's law F = -ka, where a is the displacement of the mass at time t (and hence can be denoted r(t)), which is the same as the amount by which the spring is stretched or compressed, yields d²x dt² m- -kr The motion is started by displacing the mass from the equilibrium by 1, holding it there, and then at time t= 0 carefully releasing it, so that the initial velocity is 0. In other words, the initial condition is: x(0) = =1, and (0) = 0.
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