3. We return to the problem of the plucked string discussed in Chapter 1. Show that the initial condition f is equal to its Fourier sine series 2h sin mp f(r) = Am sin mx with Am m² p(a – p)' m=1 [Hint: Note that |A„|

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A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: 15.4 Associated Legendre Equation Table 15.3 Associated Legendre Functions P(x) = -(1-x²) 1/2 = -…

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Q: 1. The periodic function f(x) has period 27. It is defined in the interval 0≤x≤ by f(x) = 2x² (a)…

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Q: press cos x √3sina in the form of Asin(x − a) with 0 < a <

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A: We first distribute the integration

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Q: 62.

A: Part (a) Rewrite the given integral: ∫tan2nx dx=∫tan2n-2xtan2x dx

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Q: f indd Pm in tev ms of @m-l and @gtl n+l -ax dx m,n-1 dx I. Cm, m-l= Hint: Recursive Method Matrid…

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Q: 13. Let the function f (x) be 2n-periodic and suppose it is represented by the Fourier series: f (x)…

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Q: Jx(-x), 0SIST 13. Find Fourier Series expansion of 1(x)31x(n+x), -nsxS0 1 1 1- 33 5 7 32 Ans.…

A: Given the function fx=xπ-x0≤x≤πxπ+x-π≤x≤0

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Q: 3. Compute sine and cosine Fourier transforms of the following function. fax+b0 [ +8 (3)

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Q: f (x)°dx

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Q: Show that in (5.2) the average values of sin mr sin nx and of cos mI cOs na, m+ n, are zero (over a…

A: Given problem is :

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A: NOTE: Refresh your page if you can't see any equations. . use the formula

Q: 2. L{sin² = nt} 7² a. S³+π²s π² b. 772 2s3-2π²s π² C. 772 2s3+2π²s π² d. S³-π²S

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Q: (b) x[n] is a periodic signal with No = 8 and the Fourier series coefficients 0, X [k] = k (mod 4) =…

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A: (.) Given function is,   h(.)  Fourier series of a function  in the interval  i.e.  is given by,…

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A: Ans- Since the square wave is only defined over a finite interval, we need to extend it periodically…