Section 9.4
Most springs are well modeled by Hooke's Law
<span> (F_{sp})_s = -k\Delta d </span>
In this relationship, it is super important to remember that there are really
two terms since \Delta s =s -s_e
where
s_e
is the equilibrium value. The equilibrium
value of the spring is not always zero.
we have seen springs already in the context of oscillations. Springs cause
oscillations because the spring force is restorative, it wants to bring you
back to the equilibrium.
The formula for work comes from integrating the variable spring force. Look at
formula 9.25 in the book. Not that the formula involves the square of the
change in position
(\Delta s_f)^2
not s_f^2
and
similarly for initial displacement.
Again a common mistake is to forget the equilibrium position
s_e
Check your Understanding.