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A massless spring (force constant k1) is suspended from
Chapter 11, Problem 11.2(choose chapter or problem)
A massless spring (force constant k1) is suspended from the ceiling, with a mass m1 hanging from its lower end. A second spring (force constant k2) is suspended from ml, and a second mass m2 is suspended from the second spring's lower end. Assuming that the masses move only in a vertical direction and using coordinates yi and y2 measured from the masses' equilibrium positions, show that the equations of motion can be written in the matrix form My = Ky, where y is the 2 x 1 column made up of yi and y2. Find the 2 x 2 matrices M and K.
Questions & Answers
QUESTION:
A massless spring (force constant k1) is suspended from the ceiling, with a mass m1 hanging from its lower end. A second spring (force constant k2) is suspended from ml, and a second mass m2 is suspended from the second spring's lower end. Assuming that the masses move only in a vertical direction and using coordinates yi and y2 measured from the masses' equilibrium positions, show that the equations of motion can be written in the matrix form My = Ky, where y is the 2 x 1 column made up of yi and y2. Find the 2 x 2 matrices M and K.
ANSWER:Step 1 of 6
Let and are the extension of the two springs from their up-stretched lengths. Let and are the extensions of two springs in the equilibrium. Hence, the displacement of the two springs from their equilibrium positions is,
Here and are the displacement of the two springs from their equilibrium positions.