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Which of the following choices is not a system equation of the following suspension system? Assume u is the displacement input, y is the displacement output; y>x>u; ๐‘ฅโ€ฒ,๐‘ฅโ€ณare the 1st order and 2nd order derivative of x,ย respectively.Group of answer choices๐น๐‘˜1=๐‘˜1(๐‘ฅโˆ’๐‘ข)All of the rest choices are correct system equations for the system๐น๐‘=๐‘(๐‘ฆโ€ฒโˆ’๐‘ฅโ€ฒ)๐น๐‘˜2=๐‘˜2(๐‘ฆโˆ’๐‘ฅ)๐น๐‘›๐‘’๐‘ก1=๐‘š1๐‘ฅโ€ณ

Question

Which of the following choices is not a system equation of the following suspension system? Assume u is the displacement input, y is the displacement output; y>x>u; ๐‘ฅโ€ฒ,๐‘ฅโ€ณare the 1st order and 2nd order derivative of x,ย respectively.Group of answer choices๐น๐‘˜1=๐‘˜1(๐‘ฅโˆ’๐‘ข)All of the rest choices are correct system equations for the system๐น๐‘=๐‘(๐‘ฆโ€ฒโˆ’๐‘ฅโ€ฒ)๐น๐‘˜2=๐‘˜2(๐‘ฆโˆ’๐‘ฅ)๐น๐‘›๐‘’๐‘ก1=๐‘š1๐‘ฅโ€ณ

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Solution

The question is asking which of the given equations is not a system equation for the given suspension system. The equations represent forces in the system, where F represents force, k and b are constants, m is mass, and u, x, and y are displacements. The primes denote derivatives with respect to time.

  1. ๐น๐‘˜1=๐‘˜1(๐‘ฅโˆ’๐‘ข): This equation represents the force exerted by the first spring, which is proportional to the difference in displacement between x and u.

  2. ๐น๐‘=๐‘(๐‘ฆโ€ฒโˆ’๐‘ฅโ€ฒ): This equation represents the damping force, which is proportional to the difference in velocity (first derivative of displacement) between y and x.

  3. ๐น๐‘˜2=๐‘˜2(๐‘ฆโˆ’๐‘ฅ): This equation represents the force exerted by the second spring, which is proportional to the difference in displacement between y and x.

  4. ๐น๐‘›๐‘’๐‘ก1=๐‘š1๐‘ฅโ€ณ: This equation represents the net force acting on the first mass, which is equal to the mass times the acceleration (second derivative of displacement).

Without additional context or information about the system, it's not possible to definitively say which of these equations is incorrect. However, if we assume that all forces and displacements are defined and calculated in a consistent manner, then all of these equations could be valid for a certain suspension system. Therefore, the answer would be "All of the rest choices are correct system equations for the system".

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