Suppose we have a thin bar of length that is insulated along the length of...

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Suppose we have a thin bar of length – that is insulated along the length of the bar and its both ends. The initial temperature is given by: u(x,0) = 0 2 - (x-7) ²³ + + 2 16 ㅠ for 0 < x < and 4 3π 4 3π for<3<3 x 4 < X < T 4 Use c = 1. (a) Find a function u(x, t) to describe the temperature at each point in the bar over time. [15 marks] (b) Use MATLAB to create a single 3-D plot showing how the temperature of the bar evolves over time. Include all terms in your solution up to n = : 10. [10 marks] Suppose we have a thin bar of length – that is insulated along the length of the bar and its both ends. The initial temperature is given by: u(x,0) = 0 2 - (x-7) ²³ + + 2 16 ㅠ for 0 < x < and 4 3π 4 3π for<3<3 x 4 < X < T 4 Use c = 1. (a) Find a function u(x, t) to describe the temperature at each point in the bar over time. [15 marks] (b) Use MATLAB to create a single 3-D plot showing how the temperature of the bar evolves over time. Include all terms in your solution up to n = : 10. [10 marks]

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