Question

Bonus question In the study of vibrations of valves used in hydraulic control systems, the valve and its elastic stem are modeled as a damped spring-mass system, as shown in Figure. In addition to the spring force and damping force, there is a fluid-pressure force on the valve that changes with the amount of opening or closing of the valve. The forcing function can be expressed as F(t) = A p(t) Derive an expression for response F(t) by means of Fourier series. [Figure: A damped spring-mass system with parameters m, c, and k is shown. The graph of p(t) is a periodic triangular wave with a period of 4? and an amplitude of 50kPa.]

          Bonus question
In the study of vibrations of valves used in hydraulic control systems, the valve and its elastic stem are modeled as a damped spring-mass system, as shown in Figure. In addition to the spring force and damping force, there is a fluid-pressure force on the valve that changes with the amount of opening or closing of the valve. The forcing function can be expressed as
F(t) = A p(t)
Derive an expression for response F(t) by means of Fourier series.

[Figure: A damped spring-mass system with parameters m, c, and k is shown. The graph of p(t) is a periodic triangular wave with a period of 4? and an amplitude of 50kPa.]

Bonus question
In the study of vibrations of valves used in hydraulic control systems, the valve and its elastic stem are modeled as a damped spring-mass system, as shown in Figure. In addition to the spring force and damping force, there is a fluid-pressure force on the valve that changes with the amount of opening or closing of the valve. The forcing function can be expressed as
F(t) = A p(t)
Derive an expression for response F(t) by means of Fourier series.

[Figure: A damped spring-mass system with parameters m, c, and k is shown. The graph of p(t) is a periodic triangular wave with a period of 4? and an amplitude of 50kPa.]

Added by James G.

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