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...

Euler's formula is used in structural engineering to determine the buckling load of columns under various conditions. However, when dealing with systems that incorporate both rigid elements and elastic components, such as springs, the analysis requires a finer approach to determine the critical load. The problem described involves two rigid bars connected at a pivot point with a spring attached and a vertical load applied at one end.
The system comprises two vertical rigid bars, AB and BC, of...

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...