Question

You are developing a diagnostic system to detect the suspension problems of some special purpose small vehicle. You will consider the suspension as a one degree of freedom. The natural frequency of the system is expected to be between 200Hz and 300 Hz. The damping ratio is between 0.05and 0.09. Evaluate the capabilities of a Fourier Transformation by developing a program. 1. Find the optimal resolution for the Fourier Transformation for the studied case. 2. Determine how small changes can be identified in the spring constant if the mass of the vehicle is only 1 kg. 3. Demonstrate how small changes can be identified in the damping coefficient of the above system. 4. Obtain the frequency response characteristics of your system by using Bode Plot and compare with the Fourier Transformation result. 5. Obtain the frequency response characteristics of the same system also by using a sweep-sine wave input. 6. Plot the calculation speed of Fourier Transformation versus FFT when you have 128, 1024, 2048and 4,096 data points.

          You are developing a diagnostic system to detect the
suspension problems of some special purpose small vehicle.
You will consider the suspension as a one degree of freedom.
The natural frequency of the system is expected to be between
200Hz and 300 Hz. The damping ratio is between 0.05and 0.09.
Evaluate the capabilities of a Fourier Transformation by
developing a program.
1. Find the optimal resolution for the Fourier Transformation for
the studied case.
2. Determine how small changes can be identified in the spring
constant if the mass of the vehicle is only 1 kg.
3. Demonstrate how small changes can be identified in the
damping coefficient of the above system.
4. Obtain the frequency response characteristics of your system
by using Bode Plot and compare with the Fourier
Transformation result.
5. Obtain the frequency response characteristics of the same
system also by using a sweep-sine wave input.
6. Plot the calculation speed of Fourier Transformation versus
FFT when you have 128, 1024, 2048and 4,096 data points.

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you are developing a diagnostic system to detect the suspension problems of some special purpose small vehicle you will consider the suspension as a one degree of freedom the natural frequen 39328

Added by Jeanette F.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Supreeta N

06/16/2023

Step 1

Optimal Resolution for Fourier Transformation:** The optimal resolution for the Fourier Transformation depends on the frequency range of interest and the desired level of detail in the frequency spectrum. * **Frequency Range:** The natural frequency of the Show more…

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You are developing a diagnostic system to detect the suspension problems of some special purpose small vehicle. You will consider the suspension as a one degree of freedom. The natural frequency of the system is expected to be between 200Hz and 300 Hz. The damping ratio is between 0.05and 0.09. Evaluate the capabilities of a Fourier Transformation by developing a program. 1. Find the optimal resolution for the Fourier Transformation for the studied case. 2. Determine how small changes can be identified in the spring constant if the mass of the vehicle is only 1 kg. 3. Demonstrate how small changes can be identified in the damping coefficient of the above system. 4. Obtain the frequency response characteristics of your system by using Bode Plot and compare with the Fourier Transformation result. 5. Obtain the frequency response characteristics of the same system also by using a sweep-sine wave input. 6. Plot the calculation speed of Fourier Transformation versus FFT when you have 128, 1024, 2048and 4,096 data points.

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Transcript

00:01 Hello students, in this question we are given a vehicle of speed.

00:05 So v is given as 40 miles per hour and we need to convert this into meter per second.

00:16 So one mile per hour is is equal to you can convert this by multiplying with 0 .44704.

00:25 So that is equal to 17 .8816 meter per second.

00:30 Now let's calculate the frequency.

00:34 So here the wavelength is given lambda is given as 10 .3 meter.

00:39 So frequency is equal to v by lambda.

00:42 So that is equal to 17 .8816 divided by 10 .3.

00:49 So that is equal to 1 .737 hertz.

00:55 So that is the frequency.

00:58 Now the magnitude and phase we can calculate.

01:01 Right.

01:02 So the magnitude the equation of motion in the frequency domain we can write down the equation of motion as m omega square plus i omega c plus k times y of omega is equal to c of omega plus k of omega times x of omega.

01:33 So here m omega is the frequency 2 pi nu.

01:39 So omega is equal to 2 pi nu 2 pi f.

01:44 So y of omega is the frequency response term of the system and c of omega is the frequency response of the dashboard.

01:53 K of omega is the frequency response of the spring and x of omega is the frequency response of the road profile.

02:00 So we can compare this equation and we get m omega square plus i omega c plus k must be equal to c omega square plus k.

02:12 So we can simplify this and you can write down m omega square plus i omega c is equal to c omega square.

02:20 Right.

02:21 The constants can be cancelled each other.

02:23 So let's substitute the values of omega in here.

02:27 So you get m.

02:29 So omega is equal to 2 pi nu.

02:33 So omega is equal to 2 pi times f which is 1 .737...

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