Write a computer code to do the mode summation for a string with a length of 20, wave velocity of 3. The string was plucked at time 0 by a source at position 8. The source function is =exp[(+)./4].

1a. Show the mode summation at time 1,2, 3 for the first 40 modes.

1b. Show the mode summation at time 1, 2, 3 for the first 80 modes.

You need to have sufficient comments in your scripts. It is not required, but is preferred to use Matlab to make a movie of the wave propagation.