The input to the valve of an internal combustion engine is a force of \(F=15,000 \mathrm{~N}\) applied over a period of \(0.001 \mathrm{~s}\) by a cam as shown in Fig. 4.59. The valve has a mass of \(15 \mathrm{~kg}\), stiffness of \(10,000 \mathrm{~N} / \mathrm{m}\), and damping constant of \(20 \mathrm{~N}-\mathrm{s} / \mathrm{m}\). The cam applies the force \(F\) once every \(0.5 \mathrm{~s}\).

(a) Find the displacement response of the valve from its rest position when the cam applies the force \(F\) for the first time.

(b) Determine the displacement of the valve from its rest position when the cam applies the force \(F\) for the second time.

Transcribed Image Text:

f(t) F O 0.001 FIGURE 4.59 Rectangular pulse force.