Solve the wave equation for the following cases: ii) For free free ends beam with following condition: ди Boundry conditions: For x = 0 and x = 1 ⇒ əx Inetial conditions: inetial desplacement: u(x, 0) = f(x): inetial velocity = g(x). ди(x,0) at 0

Q: 4. If y = tx, where t is the parameter, what are the parametric equations of the curve x' +y° = 4xy?…

A: The solution is given as

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A: In the given question, concept of line integral is applied. Line Integral An integral in which the…

Q: 2 3. (a) At any point of the curve x = t, y = t², z = t³. Find the unit tangent vector and unit…

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Q: 2. (a) Use Pythagoras' theorem to find the length of the line segment y = 2x from (1, 2) to (2, 4).…

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Q: 2. Suppose the elevation of a hilly contryside is given by the function E(z,y) = sin z + cos y. %3D…

A: The solution of given problem is followed by

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Q: 10. Find r'(1) given the following vector function. 2 3t j+ A) rf)=--i-9² j+ r'(t) : 4 -i-9t? B)…

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Q: x= 3cost +2 sint , y= e 19° parametrik denklemleri ile verilen eğrinin (3,1) noktasındaki teğet…

A: x= 3cos(t)+2sin(t) y=e6t

Q: 4. Calculate the vectors A and C curves given below with l Ádl Note: For closed curves, unless the…

A: answer is 2*pi

Q: b. -2åx + 3d, - åz 2. If E = -xả, + yåy V/m, find the work involved in moving a unit positive charge…

A: We can solve using given information and calculate the work done

Q: 8. Show that r(t) = a cost+bsint is an ellipse even if a and b are not orthogonal. How do you find…

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Q: The equatiokn  Y = (x,y)T  is given as a vectorfunction with 2 components and A = table below 3 2 2…

A: Given the initial value problem Y'=AY, Y0=y0, where A=3223. The eigenvalues are…

Q: 1. Given f(x,y) = 2x² + y² whose graph is a paraboloid. Fill in the table with the values of the…

A:

Q: x- + Y- (e) Ā = (e) Ã = + C : {y = 0, z = 0, x € (0, 0)} x² + y²' t ey x² + y2' C: {x = 0, z = 0, y…

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Q: 25. A particle is located at (1, 1,0) at time t = 0 and it follows a path whose velocity vector is…

A: Let's find.

Q: (c) Ã = xẽ, + yếy, C : {n² + y² = 1, z = 0} %3| ex (d) Ā = En + Ey 2 + 12 C : {y = x, z = 0, x € (0,…

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Q: 12. Given the vector equation [x. y] = [2.-3]+ (4.5] find a) the parametric equations b) the…

A: Given the vector equation [x, y]= [2, -3] + t[4, 5] find (a) Parametric equations (b) Symmetric…

Q: The parametric curve x(t)=t−2t6 and y(t)=t7+2t2 is given. In which case is the tangent line at the…

A:

Q: 1) How was the direction vector determined to be (1, 1, 1) if when solving for the tangent line at t…

A:

Q: Detemine the lineality over a full langth in the a-direston of he wave Sine Curve y- Asina

A: We know that the wave length of y=A sin x is 2π.  Note: The linearity over a full wave length of the…

Q: 3. (a) Two particles travel along the curves ř1 (t) = (t² + 3, t+1,6/t), ř2(u) = (4u, 2u – 2, u² –…

A: Ans 1. The two particles never collide. This can be explained with the help of the z-components of…

Q: - x=t²-t, y=t+t

A: Given query is to find the value of t where tangent line is horizontal.

Q: Q. A particle moves on the cirele x+y =I so that at time t 2 0 the position is given by the vector…

A: For the solution follow the next steps.

Q: 4. Compute the directional derivative of f(r, y) = at the point (1, 1) in a direction normal to the…

A:

Q: 7(1) = 1°i – 4tj – gk

A: we have to calculate the acceleration vector of a particle if its position vector is given as…