PhMichael
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Homework Statement
Well, I have this spring (stiffness k and free length l_{0}) mass (m ) system in a box which has a width w such that l_{0}>w (i.e. the spring is compressed). The box is excited (given a prescribed position) by: u(t)=b\cdot sin({\omega}\cdot t). Determine the range of possible frequencies \omega for which the mass does NOT lose contact with the right wall of the box.
Answer: {\omega} < \sqrt{\frac{l_{0}-w}{b}\cdot{\frac{k}{m}}}
My solution:
The acceleration of the mass is:
a=-b\cdot \omega^{2} \cdot sin(\omega \cdot t)
Therefore,
-N -k \cdot (b\cdot sin(\omega \cdot t) + l_{0} - w) = -m b \cdot \omega^{2} \cdot sin(\omega \cdot t)
Now, if I isolate N and require that N>0, 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!