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## Homework Statement

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.

## Homework Equations

[itex] T = 2 \pi \sqrt{\frac{m}{k}} [/itex]

## 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

[itex] F_{el} = ma [/itex]

[itex] k_1 x_1 = ma [/itex]

max acceration happens at aplitude:

[itex] k_1 x_1 = mA \omega ^2 [/itex]

F=ma system spring 1.

[itex] F_{el mass} - F _{el 2} = M_{s1} [/itex]

i am assuming the spring is massless ( i think we can do that)

so [itex] F_{elmass} = F_{el 2} [itex]

[itex] k_1 x_1 = k_2 x_2 [/itex]

i suppose [itex] x_1 + x_2 = A [/itex] when both x's are at maximum. ...

so [itex] \frac {k_1}{k_1} = k_2 (A-x_1) [/itex]

[itex] x_1 = \frac {A}{ \frac {k_1}{k_2} + 1 } [/itex]

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:

[itex] \omega = \sqrt{ \frac{k_1 k_2}{ (k_1 + k_1) m }} [/itex] ////

and to get F... just divide it by 2pi... right?

is this even correct?