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After Finite Element discretization of a structure, which option expresses the free vibrations equation?

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in Finite Element Method by (110k points)
After Finite Element discretization of a structure, which option expresses the free vibrations equation?

(a) Mẍ+Kẋ=F

(b) Mẍ+Kẋ=0

(c) Mẍ+Kx=F

(d) Mẍ+Kx=0

The question was posed to me during an interview for a job.

My question is taken from Eigen Value and Time Dependent Problems topic in portion Single Variable Problems of Finite Element Method

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The correct choice is (d) Mẍ+Kx=0

To explain I would say: After Finite Element discretization of a structure, the free vibrations equation can be expressed as Mẍ+Kx=0 where M and K are the mass and stiffness matrices of the structure; x and ẍ are the displacement and acceleration vectors respectively. In a free vibration analysis, the external load vector is zero.

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