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Hamilton's Modified Principle (HMP) is used to solve two nonlinear problems. The amplitude, frequency, and stability in the limit cycle of a simple pentode oscillator are calculated in order to demonstrate the principle. A standard graphical method finds the amplitude of oscillations, and results are compared with experimental data. For the case under consideration, the HMP solution gives better agreement with the experimental results Â¿ 6.6% deviation as compared with 12.4% for the graphical solution. An approximate answer is also found for the transient behavior of a nonlinear system where the input is a step function. The result is compared with an analog computer solution and shows good agreement. The solution of a simple relay servo system is indicated in which the amplitude and frequency in the limit cycle along with its stability are obtained by application of the one method of HMP.