# Find the Fourier series of the function “”##, of period ” = “# . “”##= \$%! #\$ “!&< # <&#’ \$ = \$

###### Question 1 A single machine work center has five
September 10, 2020
###### PhD course
September 10, 2020

Assignment 2: SEP291 Engineering Modelling (Submission due: 1st June 2015) 1. Find the Fourier series of the function “”##, of period ” = “# . “”##= !\$ !% < # < & \$ & < # <% ‘ \$ = ( ” # \$ %\$ 2. Find the Fourier series of the function “”##, of period ” = “# . “”##= \$%! #\$ “!&< # <&#’ \$ = \$ 3. Solve the initial value problem by the Laplace transform “! +”” = #\$ “%#&='() 4. Solve the initial value problem by the Laplace transform. If necessary, use partial fractions expansion. “!! ” ” #\$ ” = %& “‘%(= )& “!’%(= % 5. Using the formulas L ” ” #\$ = #L %”&’ “%(& or L ” “!!# = # \$ L %”&’#”%(&” “!%(&, find L ” “# if “”## equals ( ” is a constant): “#\$” . 6. Verify that the function “”##\$\$= %%& #’ + \$’ ( )+& satisfies Laplace’s equation !” ” !#” + !” ” !\$” = # and determine ” and ” so that ” satisfies the boundary conditions ” =””# on the circle “” + #” =# and ” = ” on the circle “” + #” = #\$ . 7. Find “”##\$\$ for the string of length ” =” and “” = # when the initial velocity is zero and the initial deflection with small ” (say, 0.01) is as follows: “”##= \$ \$%&”‘!##. 8. Find “”##\$\$ for the string of length ” =” and “” =# when the initial velocity is zero and the initial deflection is as follows: “”##= \$%\$&#”‘! ##.

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