Assuming we are dealing with ideal springs and dampers (that is, assuming that they behave linearly),...

  

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Assuming we are dealing with ideal springs and dampers (that is, assuming that they behave linearly), the relationships between the forces and displacements at time / are: mass: F = Mx = M* (Newton's law) spring: F= K(x-x) (Hooke's law) damper: F B = B(x-x) dr dr Using these relationships leads to the system equations, which may then be analysed using Laplace transform techniques. The mass of the mass-spring-damper system of Figure (a) below is subjected to an externally applied periodic force F(t) = 4 sin or at time = 0. Determine the resulting displacement x(t) of the mass at time t, given that x(0)=(0) = 0, for the two cases (a) w=2 (b) w=5 In the case = 5, what would happen to the response if the damper were missing? F(t) = Kx(t) F2(t)=Bx(t) K = 25 00000 B=6 M=1 F(t) = 4 sin cot M x(t) (a) F(t) = 4 sin cut (b) Assuming we are dealing with ideal springs and dampers (that is, assuming that they behave linearly), the relationships between the forces and displacements at time / are: mass: F = Mx = M* (Newton's law) spring: F= K(x-x) (Hooke's law) damper: F B = B(x-x) dr dr Using these relationships leads to the system equations, which may then be analysed using Laplace transform techniques. The mass of the mass-spring-damper system of Figure (a) below is subjected to an externally applied periodic force F(t) = 4 sin or at time = 0. Determine the resulting displacement x(t) of the mass at time t, given that x(0)=(0) = 0, for the two cases (a) w=2 (b) w=5 In the case = 5, what would happen to the response if the damper were missing? F(t) = Kx(t) F2(t)=Bx(t) K = 25 00000 B=6 M=1 F(t) = 4 sin cot M x(t) (a) F(t) = 4 sin cut (b)