A 2.25kg mass is attached to a spring and placed on a horizontal, smooth surface. A horizontal force of 20.6N is required to hold the mass at rest when it is pulled 0.215m from its equilibrium position (the origin of the x axis). The mass is now released from rest with an initial displacement of xi = 0.215m, and it subsequently undergoes simple harmonic oscillations.

a) Calculate the force constant of the spring.

b) Calculate the frequency of the oscillations in Hz.                 

c) Calculate the maximum speed of the mass                 

d) Calculate the maximum acceleration of the mass                 

e) Calculate the total energy of the oscillating system.                 

f) Calculate the speed when the displacement equals one third of the maximum value.                 

g) Calculate the acceleration when the displacement equals one third of the maximum value.