(Solved):
The equation of motion of a mass-spring system is given by mx+kx=F0sin( ...
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The equation of motion of a mass-spring system is given by mx¨+kx=F0?sin(?t+?) subjected to initial conditions x(0)=x0? and x?(0)=x?0?. Determine the expression for x(t) if m=10kg,k=1000N/m,F0?=100N,?=10rad/s,?=0,x0?=0.05m and x?0?=0.2m/s.
The complementary function is given by the general solution of the homogeneous equation: which is: where A and B are constants that can be determined from the initial conditions:
At t=0, we have: