Activity 1: The motion equation of damped mass-spring system as shown in Fig. 1 below is given as follows: dx d²x m +c+kx = f(t),t> 0 dt² dt where: x(t): displacement in meters. m: mass in kg. c: damping coefficient in kg/s. k: spring stiffness constant in N/m. t: time in seconds. f(t): external force applied on system in N. k f(t) m C Assume that: m = 2 kg, c = 3 kg/s, k = 20 N/m. Initially, assume f(t) = 0. X(t) Fig. 1: Damped mass-spring system. (1-a) Determine the general solution of x (t). (1-b) Given the initial conditions x (0) = 4, and x'(0) = 1, determine the particular solution x(t). (1-c) Use Laplace transform to solve the given differential equation with the same initial conditions given in (1-b). (1-d) Critically evaluate how your mathematical solution behaves in transient and steady sta regions. (1-e) Build a Simulink block model of the system, and generate the results of the differential equation Show the model and the results in your report and specify the transient and
Activity 1: The motion equation of damped mass-spring system as shown in Fig. 1 below is given as follows: dx d²x m +c+kx = f(t),t> 0 dt² dt where: x(t): displacement in meters. m: mass in kg. c: damping coefficient in kg/s. k: spring stiffness constant in N/m. t: time in seconds. f(t): external force applied on system in N. k f(t) m C Assume that: m = 2 kg, c = 3 kg/s, k = 20 N/m. Initially, assume f(t) = 0. X(t) Fig. 1: Damped mass-spring system. (1-a) Determine the general solution of x (t). (1-b) Given the initial conditions x (0) = 4, and x'(0) = 1, determine the particular solution x(t). (1-c) Use Laplace transform to solve the given differential equation with the same initial conditions given in (1-b). (1-d) Critically evaluate how your mathematical solution behaves in transient and steady sta regions. (1-e) Build a Simulink block model of the system, and generate the results of the differential equation Show the model and the results in your report and specify the transient and
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