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Synopsis¶

There is nothing new in this lab, but we will be putting together a few things you have seen previously. There are two pieces to this lab. For the first part, you'll use the Fourier transform function of the oscilloscope. For the second and third parts, you'll create lissajous curves using a function generator + oscilloscope setup. The primary purpose of this lab is to get further experience with encountering and getting familiar with using different pieces of equipment, in the context of waves. The third part of this lab involves basic math.

Theory¶

Looking at fourier transforms of electric signals allows for decomposing a signal into different components. It is a useful functionality of modern oscilloscopes if, for example, you want to decompose an electrical signal into different sources of high and/or low frequency noise.

A Lissajous curve is a solution to a set of equations: - $x = X_{0}\textrm{sin}(\alpha t+\delta)$ - $y = Y_{0}\textrm{sin}(\beta t)$

Procedure¶

Fourier transforms¶

Connect channel 1 of the function generator to the oscilloscope, with the generator producing a sine wave. Use the math function of the scope and produce the frequency spectrum of the measured waveforms, and compare what you see in the frequency domain with that in the time domain. How many large spikes do you see when the wave is displayed in frequency domain? At what frequency/frequencies do they occur?

• Give answer here Now, switch to a square wave. What does the wave look like in frequency domain now? At what frequencies do the spikes occur? Is this expected from theory (i.e. from the analytic fourier transform of a square wave)?
• Give answer here Now, switch to a triangle waveform. What does the wave look like in frequency domain now? At what frequencies do the spikes occur?
• Give answer here Return to the square wave. Add a phase offset of 90 degrees. How does this impact the graph of the wave in time domain? How does this impact the graph of the wave in frequency domain?
• Give answer here Now, add a DC offset to the wave. How does this impact the graph of the wave in time domain? How does this impact the graph of the wave in frequency domain?
• Give answer here Now, increase the amplitude of the wave. How does this impact the graph of the wave in time domain? How does this impact the graph of the wave in frequency domain?
• Give answer here

Oscilloscope Lissajous curves¶

Now, attach channel 2 of the function generator to channel 2 of the oscilloscope. Switch to xy mode. Set channel 1 and channel 2 to sine waves with the same amplitude. What shape is formed when the phase is the same between channel 1 and channel 2? - Give answer here Now, modify the phase of channel 2. What phase offset gives a circle? - Give answer here What shape is formed when the frequency of channel 2 is twice the frequency of channel 1? - Give answer here What phase offset gives a parabola? - Give answer here What does the shape look like when the frequency of channel 2 is 3x, 4x, and 5x that of channel 1, when there is no phase space offset? - Give answer here What does the shape look like when the frequency of channel 2 is 3x, 4x, and 5x that of channel 1, when there is a phase space offset of 90 degrees? - Give answer here Now, switch from sine waves to square waves). Check the shapes when the frequency of channel 2 is 1x, 2x, and 3x channel 1, with phase offsets of 0 or 90 degrees. What shapes are formed? - Give answer here Lastly, switch to triangle waves in each channel. Check the shapes when the frequency of channel 2 is 1x, 2x, and 3x channel 1, with phase offsets of 0 or 90 degrees. What shapes are formed? - Give answer here

Error propagation¶

What is the formula for error propagation for a quantity that is a function of "x" and "y". In other words, you have measured "x" and "y", in order to eventually measure "f(x,y)"? Write down the general formula, neglecting any correlation between "x" and "y".

• Give answer here

You are measuring the density of a material. You have measured the mass to be 1 kilogram and length, breadth and height to be 1 m (you were given a perfect cube) with instruments that were capable of measuring the mass with 1% accuracy and the length with 1% accuracy as well. What is the error on the density measurement?

• Give answer here