Answer:
a. 25 N/m
b. 0.8886 s
c. 0.707 m/s
d. At the equilibrium point
Explanation:
m = 500 g = 0.5 kg
L = 20 cm = 0.2 m
A = 10 cm = 0.1 m
a. Let g = 10 m/s2, then the gravity of the 0.5 kg book acting on the spring is
F = mg = 0.5*10 = 5 N
If the spring is stretched L = 0.2 m under 5N load, then the spring constant k is:
k = F/l = 5 / 0.2 = 25 N/m
b. We can treat this as simple harmonic motion with magnitude A = 0.1 cm. The period of this motion is
c. The book maximum speed:

d. Due to the law of energy conservation, the maximum speed would occur at the equilibrium point. This is where the potential energy, elastic energy is 0 and the kinetic energy is greatest.