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LAB_17 - Resonance

# LAB_17 - Resonance - Lab 17 Resonance"I am a skilled...

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Lab 17 187 Resonance Summary Engineering has many disciplines: mechanical, electrical, materials, chemical, civil, architectural to name a few. Though each of these areas deals with different kinds of systems, there are some similari- ties between all of them. This lab demonstrates one of these similarities using a mechanical system and an electrical system. There is a natural frequency associated with all systems, materials, circuits, buildings, even bridges. The strong reaction that occurs when an excitation is presented to a system at its natural fre- quency is called resonance. Resonance can cause a glass to break when a singer hits a note of just the right frequency. Microwave cooking and Magnetic Resonance Imaging are other examples of engineer- ing applications of resonance phenomena. Educational Objectives After performing this experiment, students should be able to: 1. Measure properties of analogs among mechanical and electrical systems. 2. Measure the resonant frequency of RLC circuits. 3. Determine the effect of changes in circuit parameters on resonant frequency. "I am a skilled designer of bridges of a sort extremely light and strong, porta- ble ladders, mortars, cannon, mines, and catapults, and in short I can contrive various and endless means of offense and defense. In times of peace I can be an architect, sculptor and can do in painting whatever may be done, as well as any other, be he whom he may be." - Leonardo da Vinci (1452-1519)

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Lab 17 188 Background Information All periodically oscillating systems have one or more natural frequencies determined by the sys- tem’s components and the configuration. The classic example of a mechanical oscillating system is shown in Fig. 1 below. Figure 1 - Mechanical oscillating system The spring is characterized by its constant k and the dashpot by its damping coefficient b . The force acting on the massive block is given by: If there is no friction, the resulting simple harmonic motion is: where A is the maximum displacement and φ is the phase angle. In the presence of friction, b >0 and the oscillations are exponentially damped. The angular frequency ω is defined as: The natural frequency ω 0 of this system is determined by the spring constant and the mass, although it can vibrate at any other frequency ω if it is forced. (1) (2) (3) (4) F kx b = − x t A t ( ) cos( ) = + ω φ x t Ae t bt m ( ) cos( ) = + 2 ω φ ω π = 2 f
Lab 17 189 The time constant τ associated with the exponential decay depends on the damping coefficient and the mass as below.

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LAB_17 - Resonance - Lab 17 Resonance"I am a skilled...

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