Consider the Mass-spring system shown in Figure 1. (a) Find the equations of motion for the...

  

Transcribed Image Text:

Consider the Mass-spring system shown in Figure 1. (a) Find the equations of motion for the system, where my and m2 are the masses of the two objects, k₁, k2 and k3 are the spring constants of the three springs. In addition, you are given that 1₁, 12 and 13 are the unstretched displacements of spring 1, spring 2, and spring 3, respectively. Rewrite the differential equations as a system of first-order differential equations, x= Ax+c, where xER¹. (b) What are the equilibrium configurations of the system for m₁3, m₂ = 9, k₁=1, k₂= 2, ks = 0.5, ₁1, 122, 3 = 1? (c) Suppose that the displacement of object 1 from the wall is 1 and its velocity is equal to 1 at t = 0. Additionally, suppose that the displacement of object 2 from the wall is 2 and its velocity is equal to -1 at time t 0. With the parameter values defined in part b), compute and plot the approximate displacements of object 1 and 2 over the time interval [0,20]. = k₁ M k₂ m₁ k3 www.my m2 Figure 1: Mass Spring system for Problem 4 Consider the Mass-spring system shown in Figure 1. (a) Find the equations of motion for the system, where my and m2 are the masses of the two objects, k₁, k2 and k3 are the spring constants of the three springs. In addition, you are given that 1₁, 12 and 13 are the unstretched displacements of spring 1, spring 2, and spring 3, respectively. Rewrite the differential equations as a system of first-order differential equations, x= Ax+c, where xER¹. (b) What are the equilibrium configurations of the system for m₁3, m₂ = 9, k₁=1, k₂= 2, ks = 0.5, ₁1, 122, 3 = 1? (c) Suppose that the displacement of object 1 from the wall is 1 and its velocity is equal to 1 at t = 0. Additionally, suppose that the displacement of object 2 from the wall is 2 and its velocity is equal to -1 at time t 0. With the parameter values defined in part b), compute and plot the approximate displacements of object 1 and 2 over the time interval [0,20]. = k₁ M k₂ m₁ k3 www.my m2 Figure 1: Mass Spring system for Problem 4

Answer rating: 100% (QA)

a The equations of motion for the system are m1x1 k1x1l1 k3x1x2 m2x2 k... View the full answer