Develop a MATLAB script to generate a 5 panel vertical plot to illustrate how a function changes as the parameters change. On ea
ch plot, display the simple sine wave, y(t) = sin(2πt), as a red line. Then, add the following functions to each of the 5-panels as black lines:
1 answer:
The question is incomplete. Complete question along with Matlab code, explanation, and output results are given below.
Complete Question:
Develop a MATLAB script to generate a 5 panel vertical plot to illustrate how a function changes as the parameters change. On each plot, display the simple sine wave, y(t) = sin(2πt), as a red line. Then, add the following functions to each of the 5-panels as black lines:
y(t) = sin(2πt) sine function
y1(t)=1+sin(2πt) effect of mean
y2(t)=2sin(2πt) effect of amplitude
y3(t)=sin(4πt) effect of frequency
y4(t)=sin(2πt) - π/4) effect of phase shift
y5(t)=cos(2πt) - π/2) relationship between sine and cosine
Step-by-step explanation:
We are required to show different sinusoidal plots to illustrate the effects of changing mean, amplitude, frequency, phase shift, and relationship of sine and cosine wave.
t=[0:0.01:2*pi] % time vector from 0 to 2pi
y=sin(2*pi*t); % the original sine function
% effect of mean
y1=1+sin(2*pi*t);
subplot(5,1,1) % 5 rows, 1 column and last for position
plot(t,y,'k',t,y1,'r') % this function plots y and y1 with respect to time vector t
% 'k' for black color and 'r' for red color
grid on
xlabel('time (t)') % x-axis is for time
ylabel('y1(t)') % y-axis is for function value y(t)
title('effect of mean') % title of the plot
ylim([-3 3]) % limit of y-axis
xlim([0 6]) % limit of x-axis
% effect of amplitude
y2=2*sin(2*pi*t);
subplot(5,1,2)
plot(t,y,'k',t,y2,'r')
grid on
xlabel('time (t)')
ylabel('y2(t)')
title('effect of amplitude')
ylim([-3 3])
xlim([0 6])
% effect of frequency
y3=sin(4*pi*t);
subplot(5,1,3)
plot(t,y,'k',t,y3,'r')
grid on
xlabel('time (t)')
ylabel('y3(t)')
title('effect of frequency')
ylim([-3 3])
xlim([0 6])
% effect of phase shift
y4=sin((2*pi*t)-pi/4);
subplot(5,1,4)
plot(t,y,'k',t,y4,'r')
grid on
xlabel('time (t)')
ylabel('y4(t)')
title('effect of phase shift')
ylim([-3 3])
xlim([0 6])
% relationship between sine & cosine
y5=cos((2*pi*t)-pi/2);
subplot(5,1,5)
plot(t,y,'k',t,y5,'r')
grid on
xlabel('time (t)')
ylabel('y5(t)')
title('relationship between sine & cosine')
ylim([-3 3])
xlim([0 6])
Output Results:
The first plot shows that sine wave gets shifted to upper side with respect to the original sine wave.
The second plot shows that the amplitude of the sine wave is increased with respect to the original sine wave.
The third plot shows that the frequency of the sine wave is increased. The number of cycles are increased with respect to the original sine wave.
The fourth plot shows there is a phase shift between two waves. The modified sine wave lags the original sine wave by π/4
The fifth plot shows the relationship between sine and cosine wave.
As we know sin(2πt)=cos(2πt - π/2)
Therefore, both waves are superimposed on each other since they are equal.
You might be interested in
Answer:
a) The best estimator for the population mean is given by the sample mean
b) The 99% confidence interval would be given by (4.969;6.431)
c) We are 99% confident that the true mean for th number of gallons of gasoline sold to his customers is between 4.969 and 6.431.
Step-by-step explanation:
1) Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
represent the sample mean for the sample
population mean (variable of interest)
represent the population standard deviation
n=45 represent the sample size
2) Part a
The best estimator for the population mean is given by the sample mean
3) Part b. Develop a 99 percent confidence interval for the population mean.
The confidence interval for the mean is given by the following formula:
(1)
Since the Confidence is 0.95 or 95%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 99% confidence interval would be given by (4.969;6.431)
4) Part c. Interpret the meaning of part (b).
On this case we can say this: We are 99% confident that the true mean for th number of gallons of gasoline sold to his customers is between 4.969 and 6.431.
Part (a)
Consecutive odd integers are integers that odd and they follow one right after another. If x is odd, then x+2 is the next odd integer
For example, if x = 7, then x+2 = 9 is right after.
<h3>Answer: x+2</h3>========================================================
Part (b)
The consecutive odd integers we're dealing with are x and x+2.
Their squares are x^2 and (x+2)^2, and these squares add to 394.
<h3>Answer: x^2 + (x+2)^2 = 394</h3>========================================================
Part (c)
We'll solve the equation we just set up.
x^2 + (x+2)^2 = 394
x^2 + x^2 + 4x + 4 = 394
2x^2+4x+4-394 = 0
2x^2+4x-390 = 0
2(x^2 + 2x - 195) = 0
x^2 + 2x - 195 = 0
You could factor this, but the quadratic formula avoids trial and error.
Use a = 1, b = 2, c = -195 in the quadratic formula.
If x = 13, then x+2 = 13+2 = 15
Then note how x^2 + (x+2)^2 = 13^2 + 15^2 = 169 + 225 = 394
Or we could have x = -15 which leads to x+2 = -15+2 = -13
So, x^2 + (x+2)^2 = (-15)^2 + (-13)^2 = 225 + 169 = 394
We get the same thing either way.
<h3>Answer: Either 13, 15 or -15, -13</h3>