Transcription of Section 3. 7 Mass-Spring Systems (no damping)
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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.
Spring force: F s is proportional to the stretch of the spring from w = k *(stretch amt) (up or down force) A weight of 4 lb stretches a spring 2 inches. The mass is displaced an additional 6 inches and then released. Construct the IVP for Undamped Free Vibration. (Use feet for the linear measure.) Mass = m 2= w/g = 4 lb/ 32ft/sec2 = 1/8 lb ...
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