PPT-Estimation of Fundamental Natural Frequency, Damping Ratio and Equivalent Mass

421L521L Lab 8 Single DOF Modeling E I L ρ E I L ρ M k c x mx cx kx ft xt Aexp ξ ω n t COS ω n sqrt 1 ξ 2 t ψ Bsin. Natural frequency and damping ratio Well consider the second order homogeneous linear constant coe57358 cient ODE bx cx with positive spring constantmass In the absence of damping term this spring constant wo 6.1.9 . 1. Equivalent ratios. 2. Find 3 additional equivalent ratios for each problem. .  . Measurement conversions. 3. 3 yd = _____in. 12 ft = _____ yd. 9 ft = _____ in. 48 in = _____ ft. 2 yd = _____ in. and. Resonance. Lecture 3. Pre-reading. : . §14.5–14.8. SHM: Vertical Springs. IMPORTANT: Set up coordinate system!!. Motion of vertical spring . is. described by simple harmonic motion with. ω = √(k/m). Applied Geophysics. 20 . Jan . 2016. © A.R. Lowry . 2016. Last time:. . Brief Intro to . Seismology . & . derivation of . the . Seismic Wave Equation. :. Four types of seismic waves:. . 1. Forced oscillator with damping. . resistance force is proportional to speed : . Equation of motion. 2. In ‘complex’ method. For convenience: . Also,. . k=m. w. 0. 2. 3. Solution of damped harmonic motion. 1. Two sine waves travelling in opposite directions .  . standing wave. Some animations . courtesy of Dr. Dan Russell, Kettering University. TRANSVERSE WAVES. ON STRINGS. Travelling transverse waves, speed of propagation, wave function, string tension, linear density, reflection (fixed and free ends), interference, boundary conditions, standing waves, stationary waves, SHM, string musical instruments, amplitude, nodes, antinodes, period, frequency, wavelength, propagation constant (wave number), angular frequency, normal modes of vibrations, natural frequencies of vibration, fundamental, harmonics, overtones, harmonic series, frequency spectrum, radian, phase, sinusoidal functions. Chapter 5. Section 5.5 and 5.6. Exploring . Ratios and . Equivalent . Fractions. INVESTIGATE. Can you compare all three at once?. Example 1.. How . many hearts to stars are there?. 16:7. 16:7. is known as a . Engineering: B.4, pages 582-588. Free Vibration. A mass is free to oscillate. No external forces acting on the mass. Amplitude, frequency, period…all constant. Natural Frequency (. f. 0. ). The frequency of the free vibrations of a system. STAT262, Fall 2017. 1. STAT262: . Ratio estimation. 2. Motivating Example: California Schools. api99 and api100. 3. Motivating Example: California Schools. Suppose that . we know . api99 for the whole population. . is a dissipation . of. . energy from a vibrating structure. .. The . term dissipate is used to . mean. . the transformation of . mechanical. . energy into other form of energy and, therefore, a removal . Objective. I can use ratio language to describe the relationship between two quantities.. Ratios. What is a ratio?. A ratio is a comparison of two quantities. (Uses division to compare two number). It shows how many times as great one quantity is to another.. Introduction. Most mechanical devices such as fans, pumps, etc. produce vibration.. Vibration is easily transmitted through solid materials and may ‘appear’ elsewhere producing troublesome vibration and/or noise.. Exercise 1. Circle any equivalent ratios from the list below. . Ratio: 1:2 . Ratio: 5:10 . Ratio: 6:16 . Ratio: 12:32.  . Find the value of the following ratios, leaving your answer as a fraction, but re-write the fraction using the largest possible unit.. Today, finishing Chapter 13:. Simple Pendulum. Circular motion and S.H.M.. Energy in S.H.M.. Damped Harmonic Motion. Driven Oscillations and Resonance.. From . http://www.cavatoyota.com/blog/what-are-shock-absorbers.