Consider a spring-dashpot system that has the following parameters: W-40 N, C-0,

Question

Consider a spring-dashpot system that has the following parameters: W-40 N, C-0, and k 0.39 N/cm. iem is may dipeced dreed how wll heytem repone (int Find he natural frequency of the system.) For the same spring-dashpot system but the coefficient of damping C has now been increased to 0.10 N/cm/s. A forcing function 4.0 sin 't drives the system where is the natural frequency of the system. (ii) Determine the equation of motion of the mass as a function of time. (iii) What is the velocity of the mass at time t= 1.2 s?

Explanation / Answer

natural frequency=sqrt(k/m)

weight, W=mg

m=40/10=4kg

k=0.39N/cm= 39N/m

natural frequency=sqrt(39/4)=3.1(k units are N/m and m in kg)

k*x+c*dx/dt=md2x/dt2

F=4sinwnt

39*x+10*ds/dt=4sin3.1t

d2x/dt2 =sin3.1t

at t=1.2 sec velocity=-cos(3.1*1.2)

so velocity=-0.99m/sec

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