a) Sketch the trajectory of a simple harmonic oscillator over the course of one period on the "phase space" plane. The y-axis is the velocity, rescaled by the square root of half of the mass. The x-axis is the position, rescaled by the square root of half of the spring constant. Explain the trajectory on subsequent periods.b) Sketch the trajectory on the same plane for a damped harmonic oscillator over the course of multiple periods.
a) Sketch the trajectory of a simple harmonic oscillator over the course of one period on the "phase space" plane. The y-axis is the velocity, rescaled by the square root of half of the mass. The x-axis is the position, rescaled by the square root of half of the spring constant. Explain the trajectory on subsequent periods.b) Sketch the trajectory on the same plane for a damped harmonic oscillator over the course of multiple periods.
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a) Sketch the trajectory of a simple harmonic oscillator over the course of one period on the "phase space" plane. The y-axis is the velocity, rescaled by the square root of half of the mass. The x-axis is the position, rescaled by the square root of half of the spring constant. Explain the trajectory on subsequent periods.
b) Sketch the trajectory on the same plane for a damped harmonic oscillator over the course of multiple periods.
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