Given a simple pendulum of length r and mass m, determine the oscillation period T if the perturbation angle θ is very small (i.e. θ < 10degrees).
How can I derive an equation for period using just that info?
2 answers
newterra.chemeketa.edu/faculty/ejensen/docs/Pendulum.doc - Similar pages - Note this
The equation of motion can be written
d(theta)/dt + (g/r) theta = 0
if the approximation sin theta = theta
is made. g is the acceleration of gravity and r is the length of the pendulum. The mass cancels out in the derivation.
The general solution of this "simple harmonic motion" differential equation is
theta = A sin wt + B cos wt
where w = sqrt (g/r)
The period is 2 pi/w
d(theta)/dt + (g/r) theta = 0
if the approximation sin theta = theta
is made. g is the acceleration of gravity and r is the length of the pendulum. The mass cancels out in the derivation.
The general solution of this "simple harmonic motion" differential equation is
theta = A sin wt + B cos wt
where w = sqrt (g/r)
The period is 2 pi/w
1 answer