Resonance. The purpose of this experiment is to observe and evaluate the phenomenon of resonance.

Transcription

1 Resonance Objective: The purpose of this experiment is to observe and evaluate the phenomenon of resonance. Background: Resonance is the tendency of a system to oscillate with greater amplitude at some frequencies than at others. Frequencies at which the response amplitude is a relative maximum are known as the system's resonant frequencies, or resonance frequencies. At these frequencies, even small periodic driving forces can produce large amplitude oscillations. Resonance phenomena occur with all types of vibrations or waves: there is mechanical resonance, acoustic resonance, electromagnetic resonance, nuclear magnetic resonance (NMR), electron spin resonance (ESR) and resonance of quantum wave functions. Resonant systems can be used to generate vibrations of a specific frequency (e.g., musical instruments), or pick out specific frequencies from a complex vibration containing many frequencies (e.g., filters). Mechanical resonance is the tendency of a mechanical system to absorb more energy when the frequency of its oscillations matches the system's natural frequency of vibration than it does at other frequencies. Each object has its own natural frequency. The resonance phenomena can cause violent swaying motions and even catastrophic failure in improperly constructed structures including bridges, buildings, trains, and aircraft. When designing objects, engineers must ensure the mechanical resonance frequencies of the component parts do not match driving vibrational frequencies of motors or other oscillating parts, a phenomenon known as resonance disaster.(see Tacoma bridge event)

2 For example, when an opera singer with a very loud voice hits the right frequency she can cause a champagne glass to resonate and break. In everyday life we encounter systems that are oscillating. Only ideal systems oscillate indefinitely. In real systems, friction forces retard the motion of these systems. Friction reduces the total energy of the system and the oscillation is said to be damped. In most physical situations, there is a nonconservative force of some sort, which will tend to decrease the amplitude of the oscillation, and which is typically proportional to the speed: This causes the amplitude to decrease exponentially with time: This exponential decrease is shown in the figure below: The image shows a system that is underdamped it goes through multiple oscillations before coming to rest. A critically damped system is one that relaxes back to the equilibrium position without oscillating and in minimum time;

3 An overdamped system will also not oscillate but is damped so heavily that it takes longer to reach equilibrium. If the driving frequency is close to the natural frequency, the amplitude can become quite large, especially if the damping is small. This is called resonance. Here we are going to focus on resonance like the one shown in the figure above. However our graphs in capstone will not produce the same as the figure. Any wave can be described by the following equation: Wave Equation ( ) ( ( ) ) (5)

4 A is the amplitude of the wave. ω is the angular frequency and t is the time. The last symbol is ( ) is the initial phase representing the value of x at t=0. From the previous lab we know that: Materials: Procedure: (1) Pasco Scientific Cart Track (1) Pasco Scientific End-Stop (2) Pasco Scientific Dynamics Track Feet ME-9872 (1) Pasco Scientific Dynamics Cart ME-9430 (1) Pasco Scientific Mechanical Oscillator/Driver ME-8750 (1) Pasco Scientific Rotary Motion Sensor CI-6538 (1) Pasco Scientific Dynamics Track Spring Set ME-8999 (1) Pasco Scientific Mass and Hanger Set ME-9348 (1) Pasco Scientific Supper Pulley ME-9448B (1) Small Rod (1) Block Clamp (1) Extech DC Power Supply (1) 1 meter of string (1) Level 1) Gather above material. 2) Attach the Track feet to the track 3) Attach the Oscillator/Driver to the end of the track labeled 0cm. Make sure you leave enough room for the bar to rotate 4) Attach the Adjustable End-Stop to same end of the track as the Oscillator/Driver 5) Attach the block clamp to the opposite end of the track (120cm mark). 6) Slide the block clamp as close to the 120 mark as possible. 7) Insert the rod into the block clamp so as the rod is vertical. 8) Attach the rotary motion sensor to the rod with a hole. Make sure

5 the large pulley on the sensor is away from the sensor. 9) Attach the supper pulley next to the block clamp. 10) The Supper pulley and rotary sensor pulley should be in line and next to each other. This step is important to make sure the line does not leave the pulley before the end of the experiment. 11) Insert the yellow plug into channel one and the black plug into channel two. 12) Level the track (both long ways and sideways) 13) Attach one end of the string to dynamics cart through the hole on top opposite the plunger. 14) Run the string down the center of the track to the motion sensor and pulley. 15) Guide the string under the bottom of the 3 position pulley on the sensor. 16) Guide the string over the top of the super pulley. 17) Finally connect the string to the mass hanger. 18) Connect the wire leader clip to the small hole on the plastic 19) Connect the spring clip to the plunger end of the dynamics cart by opening the clip and feeding the opening into the small hole next to the pin. 20) Plug in the Extech power supply. 21) Plug in the Drive motor into the power supply with red wire into red port and black wire into blue port. 22) Open the folder on your desktop labeled Capstone. 23) Open the Resonance file. 24) Turn the power supply on to 2 Volts. 25) Allow the cart to move in a uniform harmonic motion as in last lab. 26) Click 27) Slowly increase the voltage on the power supply to find at what voltage will the spring start to experience resonance 28) Allow the cart to reach its max amplitude, if any part of the experiment falls off or apart during this part then click. 29) Turn off the power supply. 30) Click the icon to scale every graph under all tabs. 31) Click the and select the Max, Min, options.

6 32) Click the and highlight the wave to just after the largest amplitude wave. 33) Click the 34) Select the Damped Sine Wave: Ae^(Bt)(sin( t+ ))+C 35) Print all Tabs using Landscape, Use recycled Paper if available. 36) Repeat step (24-32) for a total of three experimental trials. 37) Do steps (27-32) a separate piece of paper 38) Calculate the Amplitude by taking the max plus the min divided by 2 39) Calculate the period of the resonance wave (do not use capstone value) 40) Calculate the wavelength of the resonance wave(do not use capstone value) 41) Calculate the angular frequency of the resonance wave(do not use the capstone value) 42) Calculate the frequency. 43) Repeat steps (27-31) For each graph Questions: From the different trials that you conducted, how does the resonant frequency found compare with the natural frequency of oscillation. Justify your answer. Can a singer with a perfect pitch really shatter glass? Explain your answer. Soldiers normally march in unison. When approaching a bridge, the soldiers are commanded to break the step (stop marching in unison). Why? Suppose, if you repeated the same experiment with another spring of different spring constant do you observe the same resonant frequency.