Completely lost on oscillations problem

1. Jun 23, 2015

toesockshoe

1. The problem statement, all variables and given/known data
Two springs are joined and connected to a mass m such that they are all in a straight line. The two springs are connected first and then the mass last so that all three are in a row. If the springs have a stiffness of k1 and then k2, find the frequency of oscillation of m.

2. Relevant equations
$T = 2 \pi \sqrt{\frac{m}{k}}$

3. The attempt at a solution

so i tried making an F=ma for the mass and spring 1 (which is said was the spring closer to the mass)...

F=ma system mass

$F_{el} = ma$
$k_1 x_1 = ma$
max acceration happens at aplitude:
$k_1 x_1 = mA \omega ^2$

F=ma system spring 1.

$F_{el mass} - F _{el 2} = M_{s1}$
i am assuming the spring is massless ( i think we can do that)
so $F_{elmass} = F_{el 2} [itex] [itex] k_1 x_1 = k_2 x_2$

i suppose $x_1 + x_2 = A$ when both x's are at maximum. ...
so $\frac {k_1}{k_1} = k_2 (A-x_1)$

$x_1 = \frac {A}{ \frac {k_1}{k_2} + 1 }$

go back the the last equation we got in f=ma system mass and subtitute in the x_1 we just found....

the A's cancel out and after we simply we get:

$\omega = \sqrt{ \frac{k_1 k_2}{ (k_1 + k_1) m }}$ ////
and to get F... just divide it by 2pi... right?
is this even correct?

2. Jun 23, 2015

AYPHY

try it with energy method you would be albe to solve it. if not reply i will post the solution.

3. Jun 23, 2015

SammyS

Staff Emeritus

4. Jun 23, 2015

toesockshoe

do you see a problem with my solution?

5. Jun 23, 2015

SammyS

Staff Emeritus
toesockshoe,

I haven't examined your entire solution, but I'm pretty sure that your final answer IS correct !

Two springs connected in that manner have an effective spring constant of $\displaystyle\ k_\text{eff}=\frac{k_1\,k_2}{k_1+k_2}\ .$

Last edited: Jun 23, 2015