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e(ho0n3
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Here is the situation: There is a spring connected to a wall at one end and a mass m1 at the other, which in turn is connected to another spring, which is connected to mass m2, which is connected to another spring which is connected to another wall. In other words:
Wall ----- m1 ----- m2 ----- 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 x1 and x2.
(b) Determine the possible frequencies of vibration by assuming a solution of the form x1 = A1 cos ωt, x2 = A2 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:
m1a1 = -2kx1
m2a2 = -2kx2
(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?
Wall ----- m1 ----- m2 ----- 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 x1 and x2.
(b) Determine the possible frequencies of vibration by assuming a solution of the form x1 = A1 cos ωt, x2 = A2 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:
m1a1 = -2kx1
m2a2 = -2kx2
(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?