Body suspended from a linear spring

[Benzoate]

Homework Statement

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/: Go to the Homework section of the webpage, then go to assignment 5, then go to problem 5.2.

Homework Equations

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

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 definitely

$$\sqrt{k*(₁)/(m)}$$=$$\Omega$$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

 

[Benzoate]

anyone have a hard time reading my post?

 

[gabbagabbahey]

If the springs are attached in parallel, then the total restoring force is just [itex]F=F_1+F_2=k_{eff}\Delta x[/tex]. So what does that make $k_{eff}$? How about $\Omega_{eff}$?<br /> <br /> P.S. subscripts and superscripts in LaTeX are just A_{whatever} and A^{whatever}[/itex]