Figure 1 is a very powerful plot as it tells us what frequency will produce maximum steady stateresponse for our system in differential equation (1). Indeed, for the parameters here we find thatωmax = 3.24037 radians/second and the maximum steady state amplitude is 0.093352 m.a) Find the range [ωLow, ωHigh] surrounding ωmax such that all responses are at or above 90% ofthe maximum steady state amplitude of 0.093352 m. ssAmp[w] =Sqrt [Coefficient[ys[t, w], Cos[t w]]²+ Coefficient[ys[t, w], Sin[t w]]] // SimplifyWhen we finish this computation we have a nice closed form solution for the amplitude of oursteady state frequency response as a function of the input frequency w with all the other parametersof our system present as well.ssAmp(w)(2)As an example, consider the following parameters, m = 1 kg, k = 15 N/m, c = 3 N/(m/s),and Fo= 1 N. We plot the curve of Maximum Steady State Amplitude vs. Input Frequency w inFigure 1.Max SteadyState Amp0.080.060.040.025F3c²w²+k² - 2kmw² + m²w410152025Figure 1. Maximum Steady State Amplitude vs. Input Frequency.Input Frequency

Given: Ampω = F02c2ω2+k2-2kmω+m2ω4Maximum Amplitude = 0.093352

Figure 1 is a very powerful plot as it tells us what frequency will produce maximum steady state response for our system in differential equation (1). Indeed, for the parameters here we find that ωmax = 3.24037 radians/second and the maximum steady state amplitude is 0.093352 m. a) Find the range [ωLow, ωHigh] surrounding ωmax such that all responses are at or above 90% of the maximum steady state amplitude of 0.093352 m.

Figure 1 is a very powerful plot as it tells us what frequency will produce maximum steady state response for our system in differential equation (1). Indeed, for the parameters here we find that ωmax = 3.24037 radians/second and the maximum steady state amplitude is 0.093352 m. a) Find the range [ωLow, ωHigh] surrounding ωmax such that all responses are at or above 90% of the maximum steady state amplitude of 0.093352 m.