While the mass is being suspended by the magnet, the spring is neither compresse

Question

While the mass is being suspended by the magnet, the spring is neither compressed nor extended, i.e., the sprjng force is zero. The position of the mass, denoted by x, is measured from the mass center-of-gravity and is positive downward as shown. In the suspended state, the position of the mass is zero. At time t = 0, the current to the electromagnet is instantaneously reduced to zero so there is no longer a magnetic force acting on the mass. Use the following values for the system: m = 5 kg.; k = 2.8125 N/m; b = 5.25 N - sec/m; g = 9.8066 m/sec2. Initial conditions are: x(0)=0; x(0) =0. Write the system EOM for t > 0. Write the characteristic equation for the system. What is the input, or forcing function, of the system for t > 0? f(t) = u,(t)

Explanation / Answer

the equation of motion is expressed as follows:

m*d^2x/dt^2=mg-k*x-b*(dx/dt)

==> m*(d^2x/dt^2)+b*(dx/dt)+k*x=m*g

putting the values for different variables,

we get

5*(d^2x/dt^2)+5.25*(dx/dt)+2.8125*x=49

part b:

characteristic equation :

m*w^2+b*w+k=0

==5*w^2+5.25*w+2.8125=0

c) forcing function is weight of the block=m*g=49 N

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