Body suspended from a linear spring

1. Sep 30, 2008

Benzoate

1. The problem statement, all variables and given/known data

When a body is suspended from a fixed point by a certain linear spring, the angular frequency of the vertical oscillations is found to be $$\Omega$$1. When a different linear spring is used, the oscillations have angular frequency . $$\Omega$$2. Find the angular frequency of vertical oscillations when two springs are used together in parallel.

Here is a link to the problem that provides hints to the problem: http://courses.ncsu.edu/py411/lec/001/: [Broken] Go to the Homework section of the webpage, then go to assignment 5, then go to problem 5.2.

2. Relevant equations

F=k*eff*$$\Delta$$ x
$$\sqrt{k*eff/m}$$=$$\Omega$$

3. The attempt at a solution

The hint to the problem says I need to calculate restoring force for each cases.

For the parallel case, would each of the two springs exert a contact force on each other since both bodies would be attached to two different springs?

For the series case, both bodies would be in line with each other; would body would behind or in front of the other body, while sharing an attached spring; therefore I know that there is definetely

$$\sqrt{k*(1)/(m)}$$=$$\Omega$$1 ==>

$$\Omega$$1^2=$$k*1/m}$$
$$\Omega$$2^2=$$k*2/m}$$

F1= ($$\Omega$$1^2)*m*$$\Delta$$ x
F2= ($$\Omega$$2^2)*m*($$\Delta$$ x)

Not sure what my next step should be after that

Last edited by a moderator: May 3, 2017
2. Sep 30, 2008

Benzoate

anyone have a hard time reading my post?

3. Sep 30, 2008

gabbagabbahey

If the springs are attached in parallel, then the total restoring force is just $F=F_1+F_2=k_{eff}\Delta x[/tex]. So what does that make [itex]k_{eff}$? How about $\Omega_{eff}$?

P.S. subscripts and superscripts in LaTeX are just A_{whatever} and A^{whatever}