Spring Mass Oscillator

An ideal mass-spring oscillator is a physical model consisting of a massless spring that can be deformed without losing its elastic properties, called hooke spring, and a body of mass m that does not deform under the action of any force.

This system is physically impossible since a spring, however light, will never be considered a body without mass and after a certain deformation will lose its elasticity. While a body of any known substance, when applied a force, is deformed, even if it is of negligible measures.

Even so, for the conditions we want to calculate, this is a very efficient system. And under certain conditions, a mass spring oscillator can be obtained very closely.

Thus we can describe two basic spring-mass systems, which are:

Horizontal spring mass oscillator

It consists of a spring with elastic constant K of negligible mass and a block of mass m, placed on a surface without friction, as shown in the figure below:

Since the spring is not deformed, the block is said to be in an equilibrium position.

By changing the position of the block to a point in x, it will be acted upon by a restorative force governed by Hooke's law, namely:

Since the surface has no friction, this is the only force acting on the block, hence the resulting force characterizing an MHS.

Thus, the system oscillation period is given by:

When considering the surface without friction, the system will oscillate with amplitude equal to the position in which the block was abandoned in x, so that:

So we can make some observations about this system:

  • The spring-loaded block performs an MHS;
  • The elongation of the MHS is equal to the deformation of the spring;
  • At equilibrium, the resulting force is zero.