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42.3) Write down the solutions to the follig inboundary value problems for the wave equation in t...
#4.2.3 (e, f, g only) & #4.3.11 (all of it) 42.3) Write down the solutions to the follig inboundary value problems for the wave equation in the form of a Fourier series: (a) utt = uzz , u(t, 0) = u(t, π) = 0, a(0,2) 1, ut(0,x) = 0; (d) ut4u (e) ut.-uzz , u(t, 0)u1) 0, u(0,), u, (0,x; u(t, 0)=ux(t, 1)=0, a(0,2)=1, ut(0,2)=0; (g) utt = uzx , ux(t, 0)-u, (t, 1) = 0, u(0,x)-x(1-x), ut(0,2 )-0. Explain...
I need help with this PDE problem, part A and D 4.2.3. Write down the solutions to the following initial-boundary value problems for the wave equation in the form of a Fourier series: a) utt = uzz , u(t, 0) = u(t, π) = 0, u(0,x) = 1, ut(0,z) = 0; (b) utt = 2uxx, a(t, 0) = u(t, π) = 0, a(0,x) = 0, ut(0,x) = 1; c) utt = 3uzz , ti(t, 0)=u(t, π)=0, u(0,x) = sin3 x,...
Write down, but do not solve, the equation for the amounts x(t), y(t) lbs. of salt in the two tanks respectively as shown below. All valves A, B, C, D are opened at t=0 minutes. Question 3 (3 points) Saved Write down, but do not solve, the equation for the amounts x(t), y(t) lbs. of salt in the two tanks respectively as shown below. All valves A, B, C, ID are opened at t 0minutes D 2 gal/min Initial Vol.:...
Consider the initial value problem for the one-dimensional wave equation Write as clear as Ou Ou ot (4) possible , some work has been hard to follow Thanks! a(z,0) = e-r2 (a) Determine the solution u(r,t) of (4) (b) Sketch the solution in the xu-plane at t = 0, t = 1 , and (c) Which direction does the wave travel? 2
Write an equation for a sine wave with amplitude 0.129 m, wavelength 0.200 m, and wave speed 6.89 m/s traveling in the -x-direction. y(x, t) = (a m)sin[(b s^-1)t + (c m^-1)x] where a = b = c =
Write an equation for a sine wave with amplitude 0.120 m, wavelength 0.293 m, and wave speed 6.41 m/s traveling in the -x-direction. y(x,t) = (a m)sin[( b s-1)t + (c m-1)x] where a = b = c =
26 Find the solutions of the following initial-value problems: (a) cos(x + t)| _ + 1 | + 1 0, x(0) π 3 (b) 3(x + 2012ー+ 6(x +21)]/2 + 1 = 0. dt x(-1) 6
A. Write down the differential equation describing the circuit for an arbitrary time-dependent voltage V (t), in terms of the inductance L, capacitance C and resistance R of the circuit. B. Determine an analytic solution when the voltage is switched off [V(t) = ol. First, express your solution in terms of arbitrary coefficients as appropriate. Then, determine those coefficients for the initial conditions where the current is given by I(に0)-10 and satisfies I'(t = 0) = 0. C. Determine the...
A. Write down the differential equation describing the circuit for an arbitrary time-dependent voltage V (t), in terms of the inductance L, capacitance C and resistance R of the circuit. B. Determine an analytic solution when the voltage is switched off [V(t) = ol. First, express your solution in terms of arbitrary coefficients as appropriate. Then, determine those coefficients for the initial conditions where the current is given by I(に0)-10 and satisfies I'(t = 0) = 0. C. Determine the...