To understand the behavior
of a system at resonance we have to know how this system behaves when
is oscillating in a free way, that is to say, without any external
acting on it.
Let us have a look to the
most simple system: The harmonic oscillator composed of a mass linked
a spring in an horizontal plane. If we denote by x the position of the
mass relative to that corresponding to the equilibrium one, the
describing the evolution of the system is:
In this differential equation
k is the spring constant, m the mass connected to the spring and g
the friction (losses) that the environment exerts on the vibrating
The equation states that the acceleration of the mass is (1/m) times
force from the spring, proportional to the displacement of the mass
to its equilibrium position, plus a resistive force proportional to the
velocity of the mass.
Click the START button to
start an animation corresponding to an undamped oscillation (zero
Look at the time diagram
to have a look to the time evolution of the position,
x, of the particle: a sinusoidal curve.
Play with the simulation,
change the mass of the particle and observe the result.
- NOTE: For a change in, for instance, the
being accepted, you have to write the new value and press the return