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1 # Harmonic Oscillator

2 # A mass m is subject to a force F=-k*r.

3 # What is the trajectory if the mass starts at position (a,0,0)?

4 # How much time does it take to pass through zero?

5 # What is the trajectory if it starts at (a,0,0) with velocity (0,v0,0)?

6 # Compare to the case including gravity on earth in x direction

7 # m*x'' = -k*x + g

8 # m*y'' = -k*y (z can be set to 0).

10 coefficient.1(-1) -> -a # (a,0,0), has to be negative because x' is negative

11 coefficient.2 -> k/m_x # k/m for x

12 coefficient.3(+1) -> v0 # (0,v0,0), has to be positive because y'' is positive

13 coefficient.4 -> k/m_y # k/m for y, identical to k/m for x

14 coefficient.5(-1) -> -g # g

16 iintegrate x'' -> -x'

17 iintegrate -x' -> x

18 IC: -a

19 cmultiply (k/m_x, x) -> k/m*x

20 isum (k/m*x, -g) -> -k/m*x+g

21 assign (-k/m*x+g) -> x''

23 iintegrate y'' -> -y'

24 IC: v0

25 iintegrate -y' -> y

26 cmultiply (k/m_y, y) -> k/m*y

27 invert (k/m*y) -> -k/m*y

28 assign (-k/m*y) -> y''

30 output x -> out.x

31 output.y -> out.y