3. The physical pendulum. (a) In class, we derived the formula for the frequency of the physical pendulum W= Mgl I (1) Show that the expression for the frequency of the simple pendulum is consistent with this. Then derive (1) using the energy method, where the total energy is the sum of the rotational kinetic energy 1/1 (de/dt)2 and the potential energy of the centre of mass mghem. To obtain the result you will need to use the small angle expression for cosine: cos 01 02/2, for 0 <1. ― (b) A thin square plate of side L and mass M is hanging from a pivot that is drilled into one of its corners. The pivot passes perpendicularly through the plate. The plate is then lightly tapped and starts to undergo small oscillations. Using the energy method, determine the period of the oscillation, making the small angle approximation. The moment of inertia for an axis running through the centre of a square plate is ICM = ML²/6.

3. The physical pendulum. (a) In class, we derived the formula for the frequency of the physical pendulum W= Mgl I (1) Show that the expression for the frequency of the simple pendulum is consistent with this. Then derive (1) using the energy method, where the total energy is the sum of the rotational kinetic energy 1/1 (de/dt)2 and the potential energy of the centre of mass mghem. To obtain the result you will need to use the small angle expression for cosine: cos 01 02/2, for 0 <1. ― (b) A thin square plate of side L and mass M is hanging from a pivot that is drilled into one of its corners. The pivot passes perpendicularly through the plate. The plate is then lightly tapped and starts to undergo small oscillations. Using the energy method, determine the period of the oscillation, making the small angle approximation. The moment of inertia for an axis running through the centre of a square plate is ICM = ML²/6.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter39: Relativity

Section: Chapter Questions

Problem 1PQ

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