I understand the derivation for the simple harmonic motion equation:
F = -kx ( in a 1-D case)
acceleration = x''(t) = (-k/m)x
so x''(t) + (k/m)x = 0
But why is the solution to this equation
x = A cos (wt + ∅ )
How does one come up with this solution? I tried understanding this by reading my textbook however I get very confused. Any help is appreciated. Thank you.
F = -kx ( in a 1-D case)
acceleration = x''(t) = (-k/m)x
so x''(t) + (k/m)x = 0
But why is the solution to this equation
x = A cos (wt + ∅ )
How does one come up with this solution? I tried understanding this by reading my textbook however I get very confused. Any help is appreciated. Thank you.