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).

  • Successful_Try543@feddit.org
    2·
    5 months ago

    That’s why one usually searches for non trivial solution of differential equations. The trivial solution f(x)=0, in physics: “nothing happens”, is usually not of interest, as we know by experience that something must happen to a system when some initial action is performed, yet mathematically it is always there.