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Section 3. 7 Mass-Spring Systems (no damping)

Section 3. 7 Mass-Spring Systems (no damping) Key Terms/ Ideas: hooke s law of Springs Undamped Free Vibrations (Simple Harmonic Motion; SHM also called Simple Harmonic Oscillator) Amplitude Natural Frequency Period Phase Shift Warning: set your calculator for trig functions to radians NOT degrees. Simple model for Mass-Spring Systems . We will use this as our generic form of the mass spring system. Figures adapted from the work of Dr. Tai-Ran Hsu at SJSU and Wikipedia. We will study the motion of a mass on a spring in detail because an understanding of the behavior of this simple system is the first step in the investigation of more complex vibrating Systems . Natural length of the spring with no load attached. We attach a body of mass m, and weight mg, to the spring. The spring is stretched an additional L units. The body will remain at rest in a position such that the length of the spring is l + L.

Hooke’s law of springs says for small displacements that force F s is proportional to the length of the stretch in the spring. The proportionality constant is a positive value denoted by k > 0 so F s ... Undamped Oscillations are used. We are assuming that things like air resistance and

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