Figure 4 shows a mechanical system with the parameter values mass m = 1 kg, damper...

 

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Figure 4 shows a mechanical system with the parameter values mass m = 1 kg, damper b = 4 Ns/m, and spring k = 3 N/m. x(t) b F(t)- m m k Figure 4 (a) Draw the free body diagram. (b) (c) (d) Write the system and element equations. Hence obtain the differential equation relating the output displacement x(t) to the input force F(t) with the given parameter values m, b and k. dt A force F(t)=9N is applied for time t 0, with initial conditions x(0) = 0 and dx(0) = 1. Apply Laplace transform method to obtain an expression for the displacement x(t). Find the time-domain of the expression obtained in part (c) and sketch the approximate response curve, indicating clearly the initial and the steady-state values. Figure 4 shows a mechanical system with the parameter values mass m = 1 kg, damper b = 4 Ns/m, and spring k = 3 N/m. x(t) b F(t)- m m k Figure 4 (a) Draw the free body diagram. (b) (c) (d) Write the system and element equations. Hence obtain the differential equation relating the output displacement x(t) to the input force F(t) with the given parameter values m, b and k. dt A force F(t)=9N is applied for time t 0, with initial conditions x(0) = 0 and dx(0) = 1. Apply Laplace transform method to obtain an expression for the displacement x(t). Find the time-domain of the expression obtained in part (c) and sketch the approximate response curve, indicating clearly the initial and the steady-state values.