Example: Mass on a Spring

Question: A 0.20 kg mass is suspended on a spring which stretches a distance of 5.0 cm. The mass is then pulled down an additional distance of 10 cm and released. What is

a) the period of oscillation
b) the equation of motion
c) the total energy of the system
d) the displacement of the mass at t = T/6 s ?

Answer:·

• First get the spring constant:
• Now get the period:
• The equation of motion: y = Acos(wt),

  We have A = -10 cm at t = 0, but we need w:

  
• The total energy: E = kA² = $\cdot$ (39.2 N/m) $\cdot$ (0.10m)² = 0.20 J


• The displacement at t = T/6 = 0.45s/6 = 0.075 s is: y(0.075 s) = - 10 cos(14 s^-1 $\cdot$ 0.075 s) = - 5.0 cm