Consider the 1D pressure diffusivity equation: at with OSXSL and DO Boundary conditions: p(0.1) = 0, and p(2:0) = 0 Initial condition: p(x,0) = 100 By using the analytical solution; - NA L f P(x,1)= (P2 - P.)* + P2 + (P2(-1)" p) sin e L Me 117 L And/or general solution -00 -e 1-1 u(x,t)= B sin nax -4447 L a) Let L=1, a = 0.5, time step At=0.1. Please use MATLAB to plot the pressure profiles of the first 5 times (0.1,0.2, 0.3, 0.4, and 0.5). Please also plot the signals from the first three frequencies (n=1, n=2, and n=3) separately at the 5 times. Then compare the overall pressure profile (sum from n=1 to n=1000) with the signal from n=1. What can you see and why? b) Please check the signal from n=2. What do you see and why? Please check the amplitude of the signal from n=3 and compare it with that of n=1. What do you see and why? c) Now, change At to 0.01 so the first 5 times will become 0.01, 0.02, 0.03, 0.04, and 0.05. Please repeat the process in question (a). What difference (compared to question [a]) do you see and why? Please paste your MATLAB code as well as the pressure plots. Consider the 1D pressure diffusivity equation: at with OSXSL and DO Boundary conditions: p(0.1) = 0, and p(2:0) = 0 Initial condition: p(x,0) = 100 By using the analytical solution; - NA L f P(x,1)= (P2 - P.)* + P2 + (P2(-1)" p) sin e L Me 117 L And/or general solution -00 -e 1-1 u(x,t)= B sin nax -4447 L a) Let L=1, a = 0.5, time step At=0.1. Please use MATLAB to plot the pressure profiles of the first 5 times (0.1,0.2, 0.3, 0.4, and 0.5). Please also plot the signals from the first three frequencies (n=1, n=2, and n=3) separately at the 5 times. Then compare the overall pressure profile (sum from n=1 to n=1000) with the signal from n=1. What can you see and why? b) Please check the signal from n=2. What do you see and why? Please check the amplitude of the signal from n=3 and compare it with that of n=1. What do you see and why? c) Now, change At to 0.01 so the first 5 times will become 0.01, 0.02, 0.03, 0.04, and 0.05. Please repeat the process in question (a). What difference (compared to question [a]) do you see and why? Please paste your MATLAB code as well as the pressure plots