Question

  • Find the function f such that f'' = -f
  • Show that the function can be written in format f = A sin(x + B)

Extension

Find a function g such that g'' = C * -g and

  • g(0) = D
  • g'(0) = 0 where C and D are arbitrary constants.
For those who have finished the extension

Congratulations, you have just derived the formula for objects in simple harmonic motions (physics).

  • @[email protected]
    3•20 days ago

    For simplicity, I restricted my solution to the ‘extension’ part and embedded the first part into it.
    I hope it is OK to upload it here.
    The task is a neat example to train the procedure of finding a solution to ODEs with initial value problems.

    Thank you!

    Solution.