Consider a two-mass-spring flexible mechanical system given below. 21 24 In the system, u(t) is...

 

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Consider a two-mass-spring flexible mechanical system given below. 21 24 ŵ In the system, u(t) is the input force, k = 1 is the spring constant, x₁ and x2 are, respectively. the displacements of Mass 1 and Mass 2, which have masses of m₁ = m₂ = 1. Assume that there is no friction on the surfaces. X2 Mass 1 Mass 2 (a) Drive a differential equation of the mechanical system in terms of the displacement of Mass 2, i.e. x₂. (b) Assuming that u(t) = 1 and the masses are initially stationary, show that x₂ (1) = 0.25/² is a solution to the differential equation obtained in (a). (c) Same as in (b) but we now assume u(t) is a unitary impulse function. What is the analytical expression of x2(t)? [hint: Use inverse Laplace transform table] (d) Repeat (a) when the viscous friction coefficients are the same value 0.1. Consider a two-mass-spring flexible mechanical system given below. 21 24 ŵ In the system, u(t) is the input force, k = 1 is the spring constant, x₁ and x2 are, respectively. the displacements of Mass 1 and Mass 2, which have masses of m₁ = m₂ = 1. Assume that there is no friction on the surfaces. X2 Mass 1 Mass 2 (a) Drive a differential equation of the mechanical system in terms of the displacement of Mass 2, i.e. x₂. (b) Assuming that u(t) = 1 and the masses are initially stationary, show that x₂ (1) = 0.25/² is a solution to the differential equation obtained in (a). (c) Same as in (b) but we now assume u(t) is a unitary impulse function. What is the analytical expression of x2(t)? [hint: Use inverse Laplace transform table] (d) Repeat (a) when the viscous friction coefficients are the same value 0.1.

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