Consider a rectangular membrane with fixed boundaries of dimensions 5 (horizontal)by 3 (vertical). The deflection u(x, y, t) satisfies the equation utt = 6(uxx + Uyy).(a) Find a formula for the deflection u(x, y, t), if the initial velocity g(x, y) is zeroand the initial displacement f(x, y) isf(x, y) = u(x, y, 0) = 2 sin(5πx) sin(лy) - 4 sin(2x) sin(3лy)Do not show the separation of variables. Start with the formula for u(x, y, t).You need to show all details of integration or superposition (if it applies) for credit.(b) Find a numerical approximation for u(5/2, 3/2, 2).

May this answer helpful to you.

Answered: Consider a rectangular membrane with…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and y = 2 – x if 8 (x,y) = (7)x + (5)y + C .
The temperature at the point (x, y) on a metal plate is given by T (x, y) = y/(x2 + y2 ). Findthe direction and the value of greatest increase in heat from the point (4, 3).
Integrate f(x, y, z) = 2x – 3y? – 2z+3 over the line segment from the origin to (1, 1, 1) and over the line segments from the origin to (1, 1,0) and from (1, 1,0) to (1, 1, 1). -
Solve
Find the maximum rate of change of f at the given point and the direction in which it occurs for f(x, y, z) = 3x + 7y at (1,7,-1). Z Enter the maximum rate of change into R and enter the direction vector of length 1 into v as a 1x3 array.
Suppose that z is an implicit function of x and y in a neighborhood of the point P = (0, −3, 1) of the surface S of equation: exz + yz + 2 = 0 An equation for the tangent line to the surface S at the point P, in the direction of the vector w = (3, −2), corresponds to:
Suppose that over a certain region of space the electrical potential V is given by the following equation. V(x, y, z) = 4x² - 2xy + xyz (a) Find the rate of change of the potential at P(4, 6, 4) in the direction of the vector v = i + j - k. 28 √3 (b) In which direction does V change most rapidly at P? (c) What is the maximum rate of change at P? 4√ 161
Differentiate R(t) = (2t + e)(3 - Vi). Answer: R' (t) :

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS