The second-order, linear, nonhomogeneous constant-coefficient differential equation (often referred to as a forced harmonic oscillator) has a

Question:

The second-order, linear, nonhomogeneous constant-coefficient differential equation

dx dt dx dt + 250- + @x = F cos t

(often referred to as a forced harmonic oscillator) has a response

()Fcos(t  ), where A()

is often called the frequency response (strictly it is the amplitude response or gain spectrum) and is given by (10.55) and shown in Figure 10.27. How does the frequency response of the second-order, nonlinear, nonhomogeneous constant-coefficient differential equation

dx dt + 250 dx dx dt dt P +00x = F cos Qt

differ from that of the linear one?


Equation 10.55

() 1 [(w  ) + 45wQ1/ (10.55)

Figure 10.27 The response of damped second-order systems to sinusoidal forcing. A(22) A (0) 5.0 4.0 3.0 2.0

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