Problem 2. Solve the following ID wave equation: Ott(x,t) = 0xx(x, t) with the boundary conditions...
Problem 1. Find the general solution of an ID heat equation: Tt(x,t) = 4Txx(x,t) with the boundary conditions T(0,t) = T(2,t) = 0. Note that T(x,t) denotes the temperature profile along x of a uniform rod of length 2. Problem 2. Solve the following ID wave equation: Ott(x,t) = 0xx(x,t) with the boundary conditions 0 (0,t) = 0;(1,t) = 0, where 0(x,t) refers to the twist angle of a uniform rod of unit length. Problem 3. Show that the solution...
mechanical engineering
analysis help, please show all work, thanks.
Problem 2. Solve the following 1D wave equation: Ott(x,t) Oxx(x,t) with the boundary conditions 0(0,t) = 0x(1,t) = 0, where 0 (x, t) refers to the twist angle of a uniform rod of unit length.
Solve the following 1D wave equation: ?tt (?, ?) = ?xx= (?, t) with the boundary conditions ?(0, ?) = ?x(1, ?) = 0, where ?(?, ?) refers to the twist angle of a uniform rod of unit length.
Problem 1. Find the general solution of an 1D heat equation: T(x, t) = 4Txx(x, t) with the boundary conditions T(0,t) = T(2,t) = 0. Note that T(x,t) denotes the temperature profile along x of a uniform rod of length 2. Problem 2. Solve the following 1D wave equation: 0ct(x, t) = 0xx(x, t) with the boundary conditions 0(0,t) = 0,(1,t) = 0, where 8(x, t) refers to the twist angle of a uniform rod of unit length. Problem 3....
Torsional vibration of a shaft is governed by the wave equation, where x, t) is the angular displacement (angle of twist) along the shaft, x is the distance from the end of the shaft and t is time. For a shaft of length 4T that is supported by frictionless bearings at each end, the boundary cond itions are Ox(0, t) 0x(4T, t) = 0, t 0 Suppose that the initial angular displacement and angular velocity are Of(x, 0) = 1...
governed by the wave equation, Torsional vibration of a shaft at2 ax2 where x, t) is the angular displacement (angle of twist) along the shaft, x is the distance from the end of the shaft and t is time. For a shaft of length 4T that is supported by frictionless bearings at each end, the boundary conditions are t > 0 ex(0, t) 0x(47, t) = 0, Suppose that the initial angular displacement and angular velocity are e(x,0) = 3...
Torsional vibration of a shaft is governed by the wave equation = 16- where e(r,t) is the angular displacement (angle of twist) along the shaft, is the distance from the end of the shaft and t is time. For a shaft of length 3T that is supported by frictionless bearings at each end, the boundary conditions are 0 r (0,t) = 0x(3mT, t) = 0, t > 0. Suppose that the initial angular displacement and angular velocity are e(xr,0)= 4cos(4x),...
Torsional vibration of a shaft is governed by the wave equation, = 16 where (x,t) is the angular displacement (angle of twist) along the shaft, ar is the distance from the end of the shaft and t is time. For a shaft of length 2T that supported by frictionless b end, the boundary conditions are 0r(0,t) = 0x(2T, t) = 0, t> 0. Suppose that the initial angular displacement and angular velocity are (x,0) = 6 cos(x), Ot(x,0) =3+2 cos(42),...
Torsional vibration of a shaft is govened by the wave equation, dr2 dr2 f twist) along the shaft, x is the distance from the end of the shaft and t is time. For a shaft of length 4x that is supported by frictionless bearings at each end, the boundary conditions are where (x, f) is the angular displacement (angle t 0. 0x (0, )= 0x(4, )= 0, Suppose that the initial angular displacement and angular velocity are x, 0) 2...
Torsional vibration of a shaft is governed by the wave equation, = 4 where ex, ) is the angular displacement (angle of twist) along the shaft, x is the distance from the endc the shaft and is time. For a shaft of length 4x that is supported by frictionless bearings at each end, the boundary conditions are Ox(O.t) = 0x(4r, f) = 0, 1>0. Suppose that the initial angular displacement and angular velocity are Ox, 0) = 6 cos(x), 0x,...