Here is the situation: There is a spring connected to a wall at one end and a mass m(adsbygoogle = window.adsbygoogle || []).push({}); _{1}at the other, which in turn is connected to another spring, which is connected to mass m_{2}, which is connected to another spring which is connected to another wall. In other words:

Wall ----- m_{1}----- m_{2}----- Wall

where ----- represents a spring (all with spring constant k). Here are the questions:

(a) Apply Newton's 2. law to each mass and obtain two differential equations for the displacements x_{1}and x_{2}.

(b) Determine the possible frequencies of vibration by assuming a solution of the form x_{1}= A_{1}cos ωt, x_{2}= A_{2}cos ωt.

(a) There are only two forces acting on the masses in the horizontal direction, namely the spring force, so I figured the equations are:

m_{1}a_{1}= -2kx_{1}

m_{2}a_{2}= -2kx_{2}

(b) The frequencies are:

[tex]f_1 = \frac{1}{2\pi}\sqrt{\frac{2k}{m_1}}[/tex]

[tex]f_2 = \frac{1}{2\pi}\sqrt{\frac{2k}{m_2}}[/tex]

Somehow I don't think it would be this easy. Maybe I'm missing something? What do you think?

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# Homework Help: Three Springs and Two Masses

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