Question

A physical pendulum (some sort of a gadget on a hinge) installed on the international space station (ISS) has oscillation frequency ω1 = 2π/T1 when the station is on the ground (with free fall acceleration present). To provide stability in flight, a stretched spring is attached to the lowest tip of the pendulum to connect it with the point on the floor directly below the pivot point. On the ground, the entire contraption has oscillation frequency ω2 > ω1 (both free fall acceleration and the spring are in effect). Find the oscillation frequency ω of the pendulum when the ISS is in orbital flight so that the effective free fall acceleration be zero. hint: You can assume values for any parameters of the pendulum and of the spring, but the answer can be expressed just in terms of ω1 and ω2

Answer 1

This we can solve using Lagrangain approach

When pendulum is in orbigal flight, We consider kinetic energy as follows: