Consider a mass-spring-damper system shown in Figure 3 with spring stiffness k=2

Question

Consider a mass-spring-damper system shown in Figure 3 with spring stiffness k=2000 N/m, mass m=5 kg, and the damping constant c 20 N-s/m. The system is subjected to harmonic force F(t) 1000 sin10t N. (1) Obtain the steady state response of the system. (2) Determine the logarithmic decrement of the system. (3) Assume the first peak amplitude x1=1, find the peak amplitude after 10 cycles X11 Consider a mass-spring-damper system shown in Figure 3 with spring stiffness k 2000 N/m, mass m 5 kg, and the damping constant c 20 N-s/m. The system is subjected to a harmonic force F(t) 1000 sin10t N. ATI (1) Obtain the steady state response of the system. (2) Determine the logarithmic decrement of the system (3) Assume the first peak amplitude Xi - 1, find the peak amplitude after 10 cycles X11. Figure 3

Explanation / Answer

given ,

mass,m = 5kg

stiffness, k = 2000N/m

damping constant , c = 20 Ns/m

harmonic force , F(t) = 1000 N

The steady state response of the system , F = F(t) / m = 1000/5 = 200 m/s2

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