The vibrations of a mass of 150 g are simple harmonic. Figure shows the variation with displacement x of the kinetic energy Ek of the mass.

The vibrations of a mass of 150 g are simple harmonic. Figure shows the variation with displacement x of the kinetic energy E_k of the mass.

1. On Figure, draw lines to represent the variation with displacement x of
   1. potential energy of the vibrating mass (label this line P),
   2. total energy of the vibrations (label this line T).
2. Calculate angular frequency of the vibrations of the mass.
3. The oscillations are now subject to damping. Explain what is meant by damping.

Solution:

1. 
   
   1. A sensible shape for the line is its inverse of k.e.
   2. A straight line at 15 mJ, parallel to the x-axis.
2. (Maximum) kinetic energy = ½ mv²
   = ½mω²a₀²
   =15×10^-3=½ × 0.15 × ω² × (5.0×10^-2)²
   Angular frequency(ω) = 8.9(4) rad s^-1
3. Damping refers to the reduction in energy or amplitude within a system or the presence of an external force on a mass.