A block of mass m = 1 kg is initially connected to an ideal spring with a spring constant of (72) N/m. The system is placed in a liquid, which exerts an resistive force on the block in the form of fr = -bv with b= 0.2 N.s/m. A external driving force of 0.5 N is applied on the mass on every other second (see Fig. 2). (a) Write out the equation of motion of the block; calculate the value of the damping parameter and the natural resonance frequency with proper units. (b) Expand the driving force into Fourier series. Plot both your derived result and numerical result using FFT in Matlab. (c) Write out the position of the mass as a function of time in steady state, and visualize in Matlab. AF, (N) k=9 N/m WWW b=0.2 N s/m + X m= 1 kg 0 1 2 3 4 5 1 (sec) A block of mass m = 1 kg is initially connected to an ideal spring with a spring constant of (72) N/m. The system is placed in a liquid, which exerts an resistive force on the block in the form of fr = -bv with b= 0.2 N.s/m. A external driving force of 0.5 N is applied on the mass on every other second (see Fig. 2). (a) Write out the equation of motion of the block; calculate the value of the damping parameter and the natural resonance frequency with proper units. (b) Expand the driving force into Fourier series. Plot both your derived result and numerical result using FFT in Matlab. (c) Write out the position of the mass as a function of time in steady state, and visualize in Matlab. AF, (N) k=9 N/m WWW b=0.2 N s/m + X m= 1 kg 0 1 2 3 4 5 1 (sec)