A piezoelectric spring-mass system as a low-frequency energy harvester

One interesting characteristic of the simple harmonic motion (SHM) of an object attached to a spring is that the angular frequency, and the period and frequency of the motion, depend only on the mass and the force constant of the spring, and not on other factors such as the amplitude of the motion or initial conditions. We can use the equations of motion and Newton's second law to find the angular frequency, frequency, and period.
Consider a block on a spring on a frictionless surface. There...

To determine the energy of a simple harmonic oscillator, consider all the forms of energy it can have during its simple harmonic motion. According to Hooke's Law, the energy stored during the compression/stretching of a string in a simple harmonic oscillator is potential energy. As the simple harmonic oscillator has no dissipative forces, it also possesses kinetic energy. In the presence of conservative forces, both energies can interconvert during oscillation, but the total energy remains...

Elastic potential energy is the energy stored as a result of the deformation of an elastic object, such as the stretching of a spring. An object is elastic if it returns to its original shape and size after being deformed. 
Potential energy is also associated with the elastic force exerted by an ideal spring. The work done by this force can be represented as a change in the elastic potential energy of the spring. Thus, the work done by a perfectly elastic spring, in one dimension, depends only...