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DualCortex

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## Homework Statement

You have a forced, mass-spring system, without damping.

Spring constant = 4 N/m

weight of mass = 9.8 N

mass = 1 Kg

Find the motion X(t) of the mass if ω = 1.5 (Hz) and deduce the

maximum elongation of the spring. Sketch the vibrations X(t). Do same for ω = 1.9, 3.

Find the range of all safe frequencies ω. That is, frequencies that do

not destroy the system (spring breaks if elongated more than 0.06 m.At t = 0, system is at equilibrium/rest.

Therefore X(0) = 2.45 and X'(0) = 0.

## Homework Equations

External force: 0.04*cos(ω*t)

" ... the external frequency ω can be adjusted ... "

## The Attempt at a Solution

Diff eq should be

[tex]X\text{''}+4*X=0.04*\cos (\omega *t)[/tex]

Therefore,

[tex]X(t) = \left(2.45-\frac{0.04}{4-\omega ^2}\right) \text{Cos}[2*t]+\frac{0.04 *\text{Cos}[t *\omega ]}{4-\omega ^2}[/tex]

So, plugging in ω isn't that bad for the first part. However, I'm not sure how I am supposed to find the maximum elongation at each of the frequencies.

Thanks for any hints/help.FORGET ABOUT THIS PART: Manually (the dirty method of plugging in values), using Matlab I found ω = (19.97653, 20.0560) to be the range where the amplitude went over 0.06 cm.

**Turns out the professor made a mistake on one of his given variables, so the spring constant is actually 4 instead of 400, which makes a lot more sense. Just noticed the problem now is that either the spring should be able to be stretched longer or the mass weighs less ... will have to email my professor.**

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