The
particle will be in equilibrium when the tension is equal to the
weight.
A Level Maths Notes: M3 – Simple Harmonic Motion for a Particle Suspended on a String
Suppose we suspend a
particle of mass m from an elastic spring. The tension in the string
isThe
particle will be in equilibrium when the tension is equal to the
weight.
We have
where
x_e labels the equilibrium extension.
If the particle is pulled
down a further small distance
so
that
the resultant force on the particle will be upwards and is given by
We are taking downwards as
positive (since
is
assumed positive), but the acceleration will be upwards and negative.
Applying
gives
But
Differentiating
this twice gives
so
This is the equation of
simple harmonic motion
with