A pendulum in a non-inertial frame ?

1 Answer
Cesareo R.
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))

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