Game Physics Engine Development, 2nd Edition

106 Chapter 6 Springs and Spring-Like Things

Equation 5.1. If we added this, the mathematics would become considerably more

complex, for little visible improvement (remember, we’ re faking this in any case). So

we stick with the simplest kind of drag.

Solving the differential equation gives an expression for the position at any time

in the future:

p

t

=[p

0

cos(γt) +c sin(γt)]e

−

1

2

dt

where γ is a constant given by

γ =

1

2



4k −d

2

and c is a constant given by

c =

d

2γ

p

0

+

1

γ

˙

p

0

Substituting the time interval for t in the equations above as before, we can get a

value for p

t

, and calculate the acceleration required using Equation 6.5 as we did for

regular harmonic motio ...