|
With the small-angle approximation
the differential equation
for the motion of the pendulum
turns into
d2α/dt2
= - (g/ ) α
1. Note that this equation is independent of
the mass m.
2. Note that this equation does depend on
the acelleration g
for gravitation.
Solutions are very similar to those for the mass-spring system.
α(t) = αmax
sin(ωt)
for
ω = √ (g/)
and with the requirement that
αmax
should be small.
In the following videos Walter Lewin shows that the period of oscillation
T=2π/ω
does not depend on
αmax
as long as it is not too large
and, furthermore, that the period of oscillation
does not depend on the mass.
|
|