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Consider a system which is modelled by where F(t) represents where A and B are constants of integration. The constants A and B depend on of the system. If the input is solution is of the form u(t) = A cos(wt) + B sin(wt) +cos(wt) + t sin(wt). As shown in the function 1 cos(wt) + tsin(wt) becomes larger and larger as time passes. This is called of the values of A and B. However, if the input is system is 8 u(t)- A cos(wt) + Bsin(wt) + cos(3t). u" + 16u = F(t) and u(t) represents u(t) = A cos(wt) + Bsin(wt) w is equal to If F(t)=0 then The then the This situation is then the output of the

Consider a system which is modelled by where F(t) represents where A and B are constants of integration. The constants A and B depend on of the system. If the input is solution is of the form u(t) = A cos(wt) + B sin(wt) +cos(wt) + t sin(wt). As shown in the function 1 cos(wt) + tsin(wt) becomes larger and larger as time passes. This is called of the values of A and B. However, if the input is system is 8 u(t)- A cos(wt) + Bsin(wt) + cos(3t). u" + 16u = F(t) and u(t) represents u(t) = A cos(wt) + Bsin(wt) w is equal to If F(t)=0 then The then the This situation is then the output of the

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider a system which is modelled by where F(t) represents where A and B are constants of integration. The constants A and B depend on of the system. If the input is solution is of the form 1 u(t) = A cos(wt) + B sin(wt)+cos(wt) + tsin(wt). As shown in the function 1 cos(wt) + tsin(wt) becomes larger and larger as time passes. This is called of the values of A and B. However, if the input is system is 8 u(t) = A cos(wt) + Bsin(wt) + cos(3t). u" + 16u = F(t) and u(t) represents u(t) = A cos(wt) + Bsin(wt) w is equal to . If F(t)=0 then The then the This situation is then the output of the
Transcribed Image Text:Consider a system which is modelled by where F(t) represents where A and B are constants of integration. The constants A and B depend on of the system. If the input is solution is of the form 1 u(t) = A cos(wt) + B sin(wt)+cos(wt) + tsin(wt). As shown in the function 1 cos(wt) + tsin(wt) becomes larger and larger as time passes. This is called of the values of A and B. However, if the input is system is 8 u(t) = A cos(wt) + Bsin(wt) + cos(3t). u" + 16u = F(t) and u(t) represents u(t) = A cos(wt) + Bsin(wt) w is equal to . If F(t)=0 then The then the This situation is then the output of the
As shown in this function remains as time passes. In fact, the output is periodic with period . This situation is of the values of A and B. The difference between the two cases is that, in the first case, the frequency of the input F(t)=8cos(wt) is equal to the natural frequency of the system. |||||| Figure 1 Figure 2 dependent TT natural frequency bounded F(t)=8cos(2t) resonance Figure 1 4 2T the input unbounded 4TT Figure 2 F(t)=8cos(3t) F(t)=8cos(4t) the initial conditions the output independent F(t)=8cos(5t)
Transcribed Image Text:As shown in this function remains as time passes. In fact, the output is periodic with period . This situation is of the values of A and B. The difference between the two cases is that, in the first case, the frequency of the input F(t)=8cos(wt) is equal to the natural frequency of the system. |||||| Figure 1 Figure 2 dependent TT natural frequency bounded F(t)=8cos(2t) resonance Figure 1 4 2T the input unbounded 4TT Figure 2 F(t)=8cos(3t) F(t)=8cos(4t) the initial conditions the output independent F(t)=8cos(5t)
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