Solve for Period of Oscillation of 2 Springs with Mass Attached

[oneplusone]

Homework Statement

You have two springs with spring constants k_1 = 10 and k_2 = 20 vertically attached to a wall, and a mass of mass 3.00kg is hung from it. Find the period of oscillation.


----------------
||
|| <-- first spring, k_1 = 10
||
--
||
|| <== second spring, k_2 = 20
||
{} <== mass 3.00kg

Homework Equations

F=-kx
T = 2pi/omega

The Attempt at a Solution

Consider the second spring. We have:
F=-kx \implies 3(-9.8) = -(20)(x) \implies x = 1.47

Now the second spring undergoes a displacement of:

F=-kx \implies 3(-9.8) = -(10)x \implies x = 2.94.

So k effective is:

F = -k (x_1+x_2) \implies 3(9.8) = k(2.94+1.47) \implies k = 4.41

From here, i just found \omega by using \omega =\sqrt{k}{m}. and the period was easy from there.

Is the first part of my solution correct? I am having trouble visualizing it.

 

[Doc Al]

Consider the second spring. We have:
F=-kx \implies 3(-9.8) = -(20)(x) \implies x = 1.47

Now the second spring undergoes a displacement of:

F=-kx \implies 3(-9.8) = -(10)x \implies x = 2.94.

So far so good.

So k effective is:

F = -k (x_1+x_2) \implies 3(9.8) = k(2.94+1.47) \implies k = 4.41

4.41 is the total displacement, not the spring constant. Solve for the effective spring constant.

 

[oneplusone]

oops i meant 6.666. Thank you.

A follow up question to this has the same springs, except oriented like this:

-------------------
|| ||
|| ||
|| ||
|| ||
------
| {} |
------With the springs parallel. How would you solve this? I am still not convinced that there is a solution (to me, the "block" will be tilted).

 

[Doc Al]

With the springs parallel. How would you solve this? I am still not convinced that there is a solution (to me, the "block" will be tilted).

Assume the system is constrained so that the springs get the same displacement.