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Applied Mathematics For Engineers Assignment

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Added on  2020-01-28

Applied Mathematics For Engineers Assignment

   Added on 2020-01-28

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Applied Mathematics ForEngineers
Applied Mathematics For Engineers Assignment_1
TABLE OF CONTENTSPART 1............................................................................................................................................1Task 1.....................................................................................................................................1Task 2.....................................................................................................................................4PART 2............................................................................................................................................8Task 3.....................................................................................................................................8Task 4...................................................................................................................................11
Applied Mathematics For Engineers Assignment_2
PART 1Task 11) find the frequency, periodic time, amplitude of two wavesa) F(t) = 10 cos (4/3 t)the amplitude is the maximum value of the function, the amplitude can be defined as the maximum distance the wave can travel from its centre.Here the maximum value is 10, so the amplitude = 10to find out the period, it can be found out as period = 360 / (4/3)period = 270 degreeFrequency can be measured as the number of wave complete in each 180 degree. The frequency can be given as f = c/ λwhere,c = speed of sound, which is 343 m/s.f = frequencyλ = wave lengthhere, ω = 4/3so, f = 1/Tor it can also be written as; f = ω/2πf = (4/3)/2*3.14f = 0.21 Hznow, the time period can be given as; f = 1/Tso, T can be expressed asT = 1/fT = 1/0.21T = 4.76 seconds.b) F(t) = 10 sin (3t)here, the maximum value is 10, so it is very mush easy to find out the amplitude,amplitude of this wave = 10. the ω can be give here, which is given as 3.1
Applied Mathematics For Engineers Assignment_3
with the help of ω, we can find out the frequency. The formula of frequency given is;f = ω / 2πf = 3/2*3.14f = 0.477 Hzafter finding out the frequency, the time period can be found out here, which is T = 1/fT = 1/0.477T = 2.093 seconds. c)the displacement can be modified by any sinusoidal functions, which is given as;= 2 cos x + √3 Sin xthe new form, which will be converted into R sin (x+a), where R>0 and 0<a<90 degree. The value of R and x have to be found out here, we have to convert this equation, which can be done as;we will only take the positive sign, so that it will be easy for us to calculate;therefore;2 cos x + √3 Sin x = R sin (x+a)the formula can be applied here to open the brackets,sin(a+b) = sin A cos B + cos A sin Bin the same way, we can expand this equation as;R sin (x+a) = R (sin x cos a + cos x sin a) =R sin x cos a + R cos x sin aSo, by the above equations we can say that; √3 Sin x + 2 cos x = R cos a sin x + R sin a cos xnow, equating all the co efficient of sin and cos in the above equation, we are having;for sin x : √3 = R cos a ... (i)for cos x : 2 = R sin a ... (ii)divide equation (ii)/(i) 2/√3 = R sin a/ R cos a2/√3 = tan aa = arc tan (2/√3) a = 0.857 degree2
Applied Mathematics For Engineers Assignment_4

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