Use the 1D diffusion equation to find T(x,t):
Use the 1D diffusion equation to find T(x,t): 2. A bar of length L has an...
3. An infinite bar has initial temperature distribution: T(x,0)-T0 [s(x-l) +δ(x + 1)] Find T(x,t) for >0. The free space Green's function for the 1-D diffusion equation is G(x -x)- e 4DI 4TDt
The m1 and m2 (m1=m2=m) are attached to the ends of a string of length l. The string is going through a frictionless hole in the middle of a frictionless table. m1 is given certain initial push along the x-y plane and perpendicular to the position vector r. find the Lagrangian L and Lagrange equations of motion for the system. NG >X m2
Find the length of spiral curve T() = ----- 0 < > < 2”
Consider a thin bar of length 20 with heat distribution Tz,t), where ar 22T 36 for <I<20 and t> 0. (a) Suppose T satisfies homogeneous BCs T(0,t) = T(20, t) = 0 fort > 0, and the IC T+(3,0) = -sin for 0 <<< 20. Find T(,t) by using a separation solution similar to the one in the course notes. i. What are wr and An(n=1,2,...)? ta = (n+Pi 20 An= (6*n*Pi)/20 1. Apply the initial condition to determine T(3,t)....
7.13 Use the differential equation approach to find v.(t) for t > 0 in the network in Fig. P7.13. 4H TO + 1 = 0 2013 342 340 0.(t)
A thin flat plate of length L, thickness t, and width W> L is thermally joined to two large heat sinks that are maintained at a temperature T.. The bottom of the plate is well insulated, while the net heat flux to the top surface of the plate is known to have a uniform value of Heat sink T. Heat sink T. a) Derive the differential equation that determines the steady-state temperature distribution T(x) in the plate. b) Solve the...
Let X1, ..., Xn be a random sample from the distribution 1 f(x; 01, 02) e-(2–01)/02 x > 01, - < 01 <0, 02 > 0. 7 02 Find the method of moments estimators (MMEs) of 04 and 02.
Let X have a gamma distribution with parameters a > 2 and 3 > 0. (a) Prove that the mean of 1/X is B/(a - 1). (b) Prove that the variance of 1/X is 82/[(a - 1)(a 2)].
2. The probability density function of X is given by 10 0,x < 10 a) Find P(X>20). b) What is the cumulative distribution function of X?
Problem 6 Find the temperature in in a laterally insulated bar of length L whose ends are also insulated, assuming the same initial temperature profile as in Problem 5. Hint: remember that if the end points are thermally insulated, there is no heat flow. Hence, the temperature gradient must vanish at the endpoints! Problem 5 Find the temperature in a laterally insulated bar of length whose ends are kept at 0° Celsius, assuming that the initial temperature distribution is in...