Question

A spring-mass system consists of a 0.5 kg mass attached to a spring with a force constant of k = 8 N/m. You may neglect the mass of the spring. The system undergoes simple harmonic motion with an amplitude of 5 cm. Calculate the following: 1. The period T of the motion 2. The maximum speed Vmax 3. The speed of the object when it is at x = 3.5 cm from the equilibrium position. 4. The total energy E of the system.

Answer 1

The mass is m = 0.5 kg, the spring constant k = 8 N/m. And so, the angular frequency is
  
And the amplitude of the motion is, A = 5 cm = 0.05 m.

1)
  The period of the motion is given by
  

2)
The maximum speed is
   

3)
  The velocity as a function of position is given by
  
And so, at x = 3.5 cm = 0.035 m, the speed is given by
  
  

4)
  The total energy is