Q4) Derive the equation of motion of the system given in following figure with Lagrange
Equation and Newton's Second Law of motion. For the following data, determine the natural
frequency, the critical damping constant, the damping ratio, and calculate the response of the
system, x(t) for given initial condition.
k=10000(N)/(m),c=350N(m)/(s),m=3kg,r=0.01m,L=0.6m,x(0)=0.001m,x^(˙)(0)=0.2(m)/(s)
Q4 Derive the equation of motion of the system given in following figure with Lagrange Equation and Newton's Second Law of motion.For the following data, determine the natural frequency, the critical damping constant, the damping ratio, and calculate the response of the system,x(t) for given initial condition.
k=10000 N/m,c=350Nm/s,m=3kg,r=0.01m,L=0.6mx0=0.001m,x0=0.2m/s
2k WMM
3
Slender bar of mass m
3
Rigid massless link
M
3
Thin disk of mass m, no slip