Consider the mechanical system with a nonlinear spring shown in Figure 3. The relationship between the...

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Consider the mechanical system with a nonlinear spring shown in Figure 3. The relationship between the spring force, f(t), and the displacement, x(t), is f(t) = 2x² (t). Assume the output to be the displacement of the mass, x(t). Answer the following questions. a. (3 marks) Write the equations of motion in time domain (2nd-order differential equation). b. (2 marks) Find the equilibrium point when the applied force is f = 10 + f(t) where of (t) is a small force about the 10 N constant value. Is this point a natural equilibrium point or an operating point? Explain. c. (5 marks) Determine the linearized form of the system about the equilibrium point either in state space form (by choosing displacement x and velocity as state variables) or in transfer function form (by finding 8X(s)/8F(s)). h Nonlinear spring 0000 H 1 kg Figure 3 x(1) f(t) Consider the mechanical system with a nonlinear spring shown in Figure 3. The relationship between the spring force, f(t), and the displacement, x(t), is f(t) = 2x² (t). Assume the output to be the displacement of the mass, x(t). Answer the following questions. a. (3 marks) Write the equations of motion in time domain (2nd-order differential equation). b. (2 marks) Find the equilibrium point when the applied force is f = 10 + f(t) where of (t) is a small force about the 10 N constant value. Is this point a natural equilibrium point or an operating point? Explain. c. (5 marks) Determine the linearized form of the system about the equilibrium point either in state space form (by choosing displacement x and velocity as state variables) or in transfer function form (by finding 8X(s)/8F(s)). h Nonlinear spring 0000 H 1 kg Figure 3 x(1) f(t)

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SOLUTION a The equation of motion for the system can be derived using Newtons second law of motion which states that the sum of the forces acting on a... View the full answer