MATLAB Plotting Time Step Range for Temperature Profiles in Matlab/Mathematica

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To visualize temperature profiles over a dimensionless time interval of $t \in [0,4]$, the series approximation for temperature, T(x,t), is provided. The function incorporates a series of cosine terms with exponential decay factors. For implementation in Mathematica, users can define the function T[x, t] and create multiple plots for different time steps, such as t=0, t=0.5, and t=1, using the Plot function. The plots should be combined using the Show function to display them on the same axes. It's important to ensure that the x range is appropriate for the specific problem context to accurately represent the temperature distribution.
Dustinsfl
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Using this series approximation, plot the temperature profiles on the same set of axes for a range of time steps in the dimensionless time interval $t\in [0,4]$ in order to visualize the process.
$$
\begin{alignat*}{3}
T(x,t) & = & 1.7624\cos(0.86x)e^{-0.86^2t} - 0.1638\cos(3.426x)e^{-3.426^2t} + 0.476\cos(6.437x)e^{6.437^2t}\\
& - & 0.0218\cos(9.529x)e^{-9.529^2t} + 0.0124\cos(12.645x)e^{-12.645^2t} - 0.0080\cos(15.771x)e^{-15.771^2t}\\
& + & 0.0055\cos(18.902x)e^{-18.902^2t} - 0.0041\cos(22.036x)e^{-22.036^2t} + 0.0031\cos(25.172x)e^{-25.172^2t}\\
& - & 0.0025\cos(38.31x)e^{-28.31^2t}
\end{alignat*}
$$
How can I do this in Matlab or Mathematica?
 
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In Mathematica, you could do something like this:

f[x_,t_]=your_function
PlotOne=Plot[... at t=0]
PlotTwo=Plot[... at t=0.5]
PlotThree=Plot[... at t=1]
.
.
.
Show[PlotOne,PlotTwo,PlotThree].
 
PlotOne = Plot[f[x,0],{x,-10,10}]

Like this?
 
Exactly. Just make sure your $x$ range corresponds to the region of interest for the problem.
 

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