Consider a system which is modelled by where Ft) represents where A and B are constants...
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Consider a system which is modelled by where Ft) represents where A and B are constants of integration. The the system. If the input is As shown in As shown in situation is becomes larger and larger as time passes. This is called the input is then the output of the system is Figure 2 4m the function Figure 1 and utty represents this function remains Ft Bros(5) of the values of A and B. bounded unbounded then the solution is of the form u" +16u = F(t) u(t) = Acos(ut) + Bsin(ut) + cos(ut) + sin(urt). Figure 1 u(t)= A con(ut) + Bin(t) w is equal to F(x)=Bros(21) F-8) The difference between the two cases is that, in the first case, the frequency of the input Ft)-8cos[wt) is equal to the natural frequency of the system. IfRt-then cos(ut) + t sin(wt) u(t)= A con(ust) + Bsin(ut) + cos(3) This situation is Independent The constants A and B depend on as time passes. In fact, the output is periodic with period H the input dependent Figure 2 of the values of A and B. However, if the initial conditions natural frequency Fit-Bos/41) resonance 2m This the output Consider a system which is modelled by where Ft) represents where A and B are constants of integration. The the system. If the input is As shown in As shown in situation is becomes larger and larger as time passes. This is called the input is then the output of the system is Figure 2 4m the function Figure 1 and utty represents this function remains Ft Bros(5) of the values of A and B. bounded unbounded then the solution is of the form u" +16u = F(t) u(t) = Acos(ut) + Bsin(ut) + cos(ut) + sin(urt). Figure 1 u(t)= A con(ut) + Bin(t) w is equal to F(x)=Bros(21) F-8) The difference between the two cases is that, in the first case, the frequency of the input Ft)-8cos[wt) is equal to the natural frequency of the system. IfRt-then cos(ut) + t sin(wt) u(t)= A con(ust) + Bsin(ut) + cos(3) This situation is Independent The constants A and B depend on as time passes. In fact, the output is periodic with period H the input dependent Figure 2 of the values of A and B. However, if the initial conditions natural frequency Fit-Bos/41) resonance 2m This the output
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