QUESTION 1: The mathematical equation that describes a cosine wave as a function of time (t) is given below, where A is the amplitude of the sine wave, fn is the frequency in Hz, is the phase shift of the sine wave in radians: a) y₁ = Acos(27ft-) If = 40, and A = 10, plot the above sinusoidal function for 1 ≤t≤ 2, with different frequencies: fi = 1Hz, f2 = 2Hz. Plot the two functions on the same graph with "red dotted line" represents the function with 1Hz, and "black solid line" represents the function with 2Hz. Use a time step of 0.001. Label all the axes, include gridlines and provide a legend in your plot. b) A linear combination of sinusoidal waveforms is given below: v,(t)= A, sin(27f₁t − q ) + A₂ cos(27f₂t − ₂) Plot v(t) for 0 ≤ t ≤, with A₁ = 5, A₂ = -5, fi = 1Hz, f2 = 3Hz, 1 = 45°, 2 = 75°. Use a time step of 0.001. Label all the axes and includes gridlines in your plot. (Hint: type "help plot" in the Command Window, scroll down and choose the correct function under "see also")

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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QUESTION 1:
The mathematical equation that describes a cosine wave as a function of time (t) is given below,
where A is the amplitude of the sine wave, fn is the frequency in Hz, is the phase shift of the sine
wave in radians:
a)
y₁ = Acos(2лft-)
If = 40°, and A = 10,
plot the above sinusoidal function for 1 ≤ t ≤ 2, with different frequencies: fi = 1Hz, f2 = 2Hz. Plot
the two functions on the same graph with "red dotted line" represents the function with 1Hz, and
"black solid line" represents the function with 2Hz. Use a time step of 0.001. Label all the axes,
include gridlines and provide a legend in your plot.
b)
A linear combination of sinusoidal waveforms is given below:
v,(t)= A, sin(27ft - )+ A₂ cos(27f₂t - ₂)
Plot v(t) for 0 ≤ t ≤, with A₁ = 5, A₂ = -5, fi = 1Hz, f2 = 3Hz, 1 = 45°, 2= 75°. Use a time step
of 0.001. Label all the axes and includes gridlines in your plot. (Hint: type "help plot" in
the Command Window, scroll down and choose the correct function under "see also")
Transcribed Image Text:QUESTION 1: The mathematical equation that describes a cosine wave as a function of time (t) is given below, where A is the amplitude of the sine wave, fn is the frequency in Hz, is the phase shift of the sine wave in radians: a) y₁ = Acos(2лft-) If = 40°, and A = 10, plot the above sinusoidal function for 1 ≤ t ≤ 2, with different frequencies: fi = 1Hz, f2 = 2Hz. Plot the two functions on the same graph with "red dotted line" represents the function with 1Hz, and "black solid line" represents the function with 2Hz. Use a time step of 0.001. Label all the axes, include gridlines and provide a legend in your plot. b) A linear combination of sinusoidal waveforms is given below: v,(t)= A, sin(27ft - )+ A₂ cos(27f₂t - ₂) Plot v(t) for 0 ≤ t ≤, with A₁ = 5, A₂ = -5, fi = 1Hz, f2 = 3Hz, 1 = 45°, 2= 75°. Use a time step of 0.001. Label all the axes and includes gridlines in your plot. (Hint: type "help plot" in the Command Window, scroll down and choose the correct function under "see also")
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