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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.

Thus we have second order linear DE mu(t) ... (Assume no damping.) Determine the position u(t) of the mass at any time t. Then determine the first time the maximum magnitude will occur. The IVP: We have English units so g = 32ft/sec2 so change the inches to feet; 6 in = ½ ft,

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

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