Problem 12.17

12.17. a)
The total energy is given by
$E= \frac{1}{2} k A^{2} ~=~ .0280 J$

b)
The speed is given by
$v = \omega \sqrt{A^{2} - x^{2}}$
$v = \sqrt{\frac{k}{m}} \sqrt{A^{2} - x^{2}}$
v = 1.02 m/s

c)
The kinetic energy is given by
$K = \frac{1}{2}k A^{2} - \frac{1}{2} k x^{2}$
$K = \frac{1}{2}(35) (.04)^{2} - \frac{1}{2} (35) (.03)^{2}$
K = 12.2 mJ

d)
The potential energy is given by subtracting the kinetic from the total energy.
U = E - K
U = 15.8 mJ