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Well, I have this spring (stiffness [itex]k[/itex] and free length [itex]l_{0}[/itex]) mass ([itex] m [/itex] ) system in a box which has a width [itex]w[/itex] such that [itex]l_{0}>w[/itex] (i.e. the spring is compressed). The box is excited (given a prescribed position) by: [itex]u(t)=b\cdot sin({\omega}\cdot t)[/itex]. Determine the range of possible frequencies [itex]\omega[/itex] for which the mass does NOT lose contact with the right wall of the box.

Answer:[tex]{\omega} < \sqrt{\frac{l_{0}-w}{b}\cdot{\frac{k}{m}}}[/tex]

My solution:

The acceleration of the mass is:

[tex]a=-b\cdot \omega^{2} \cdot sin(\omega \cdot t)[/tex]

Therefore,

[tex] -N -k \cdot (b\cdot sin(\omega \cdot t) + l_{0} - w) = -m b \cdot \omega^{2} \cdot sin(\omega \cdot t)[/tex]

Now, if I isolate [itex] N [/itex] and require that [itex] N>0 [/itex], I don't get to that answer. In fact, my answer will obviously depend on this sine function too. What am I doing wrong? what is the correct approach for solving this question?

Thanks!

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# Homework Help: Spring-mass system in an excited box

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