A pendulum in a non-inertial frame ?

1 Answer
Nov 12, 2016

Considering the car as a non-inertial reference frame, the pendulum oscilates around the equilibrium position. This occurs with the rope at angle #phi# such that

#phi = arctan(a/g)#

because with the rope at this angle, the momentum of #m vec alpha = m(-a hat i-g hat j)# regarding the pendulum fulcrum is null.

Around this point, the small oscillation period must be

#T=2pi sqrt(l/norm vec alpha)#

Note that without additional acceleration should be #2pi sqrt(l/g)#

so

#T = 2pi sqrt(l/sqrt(g^2+a^2))#