Answer Happy

Figure 3.1(a) illustrates a system with a mass of m = 20 kg, damping coefficient of c =
120 N • s/m, springs stiffnesses of k, = 4800N/m, k2 = 400N/m, and k3 = 800N/m
attached to the mass placed on frictionless rollers. The system is constructed in Wolfram
System Modeller as shown in Figure 3.1 (b). If the mass is given a small displacement and
then released, the results displayed in Figure 3.2 show that the system is underdamped.
3.1. The natural frequency.
[41
3.2. The Damping ratio.
[3]
3.3. Compute the solution for the plot, by computing the constants Cr and C2 and expressing
your equation in its simplest form, if the initial displacement is X, = 0.2 m, and initial
velocity *, = 0 m/s.
Figure 3.1(a) illustrates a system with a mass of m = 20 kg, damping coefficient of c = 120 N.s/m, springs stiffnesses of ky = 4800N/m, kz = 400N/m, and kz = 800N/m attached to the mass placed on frictionless rollers. The system is constructed in Wolfram System Modeller as shown in Figure 3.1 (b). If the mass is given a small displacement and then released, the results displayed in Figure 3.2 show that the system is underdamped. 3.1. The natural frequency. [4] 3.2. The Damping ratio [3] 3.3. Compute the solution for the plot, by computing the constants C and C2 and expressing your equation in its simplest form, if the initial displacement is x = 0.2 m, and initial velocity *, = 0 m/s. [6] masst m ww W IDIOTORID (a) (b) Figure 3.1 Spring mass damper system