Effect of Speed on SteadyState Response With a 01 b 10 L

Effect of Speed on Steady-State Response

-With a = 0.1 , b = 1.0, L =88 pi and A= 1.0 ft consider automobile speeds between 8.8 and 88 ft/s. For this example choose y(0) and y\'(0)
Why can we do this? Show the response for various automobile speeds. Describe how the amplitude of the steady-state response changes with the speed of the automobile.Explain anything of interest that you see when comparing the vehicle’s speed to the amplitude of oscillation

Equation ------ y\" +ay\' +by = Asinwt + Awcoswt

The General Solution ------- y(t) =C1e^c1t + C1e^c2t +C3sinwt + C4coswt

-Maximize the Amplitude of the Steady-State Response

Suppose that an automobile weighs 3200 lb and contains a wheel assembly with a spring/damper shock absorber. Suppose the spring constant is k = 6000 lb/ft, and the damping constant is c = 200 lb-slug/ft. If the automobile encounters a sinusoidal road with a wavelength of 40 ft and an amplitude of 0.2 ft, then what speed maximizes the vibrations of the wheel?

Solution

Steady state occurs after the system becomes settled and at the steady system starts working normally. Steady state response of control system is a function of input signal and it is also called as forced response.
Now the transient state response of control system gives a clear description of how the system functions during transient state and steady state response of control system gives a clear description of how the system functions during steady state. Therefore the time analysis of both states is very essential. We will separately analyze both the types of responses. Let us first analyze the transient response. In order to analyze the transient response, we have some time specifications and they are written as follows:
Delay Time : This time is represented by t_d. The time required by the response to reach fifty percent of the final value for the first time, this time is known as delay time. Delay time is clearly shown in the time response specification curve.
Rise Time : This time is represented by t_r. We define rise time in two cases: