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acceleration amplifier amplitude analog computer apply Assuming balance becomes center of gravity characteristic equation complex considered constant control element control system crankshaft critical frequency curve damper damping ratio dead zone deflection degrees of freedom differential equations discussed in Sec displacement dynamics effect engine equivalent example feedback flywheel forcing function free vibration harmonic inertia forces input Laplace transformation lb/in linear load loci magnitude mass maximum McGraw-Hill Book Company method motion natural frequency nonlinear operation operational amplifier oscillation output pendulum phase angle phase margin phase plane plane plot poles positive Prob problem proportional control rad/sec real axis reference level root-locus roots rotating rotor shaft shaking force shown in Fig simple harmonic motion simplifying sinusoidal sinusoidal response solution speed spring rate static steady-state error step change Substituting from Eq system in Fig tion torque torsional undamped vector velocity zero