A pendulum is suspended from the cusp of a cycloid cut in rigid support. The path described by the pendulum bob is cycloidal and

Question

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A pendulum is suspended from the cusp of a cycloid cut in rigid support. The path described by the pendulum bob is cycloidal and

is given by: x = a (φ − sin φ) y = a(cos φ − 1), where the length of the pendulum is l = 4a, and where φ is the angle of rotation of the circle generating the cycloid. Shat that the oscillations are exactly isosynchronous with frequency ω0 = p g/l, independent of the amplitude.

Physics

1 answer:

oksano4ka [1.4K] · Answer 1 · 2021-11-25T15:22:29+03:00

Answer:

Verified that he oscillations are exactly isosynchronous with frequency ω0 = p g/l, independent of the amplitude.

Explanation:

Starting from the first principle for the derivation and to prove that the oscillations are exactly isosynchronous with frequency ω0 = p g/l, independent of the amplitude. The mathematical manipulations was applied, trigonometric identities was also applied.The steps and explanation are shown in the attachment.