Question: 1. Consider a rectangular membrane with fixed boundary of dimensions 3 (horizontal) by 2 (vertical). The deflection u (r, y, t) satisfies the equation utt

1. Consider a rectangular membrane with fixed boundary of dimensions 3 (horizontal) by 2 (vertical). The deflection u (r, y, t) satisfies the equation utt = 16 (Usr + Wyy) . (a) Find a formula for the deflection u (x, y, t), if the initial velocity g (r, y) is zero and the initial displacement f (x, y) is f (x, y) = u(x, y, 0) = 5sin (mx) sin (my) - 2 sin (3mr) sin (3my) Do not show separation of variables. Start with the formula for u (x, y, t) (b) Find a numerical approximation of the deflection u (1.8, 1.2, 2)

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