In class, we derived the formula for the frequency of the physical pendulum Mgl I =...

Transcribed Image Text:

In class, we derived the formula for the frequency of the physical pendulum Mgl I = لا (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 I (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 ~ 1 02/2, for << 1. A bar of length 2L is bent in the middle so that the two arms of equal length make a 90° vertex. The bent bar is then pivoted from the vertex and allowed to oscillate about its equilibrium position in the plane formed by the two arms. Using the energy method, determine the period of the oscillation. Note added March 6: Again, make the small-angle approximation. [5] [5] In class, we derived the formula for the frequency of the physical pendulum Mgl I = لا (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 I (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 ~ 1 02/2, for << 1. A bar of length 2L is bent in the middle so that the two arms of equal length make a 90° vertex. The bent bar is then pivoted from the vertex and allowed to oscillate about its equilibrium position in the plane formed by the two arms. Using the energy method, determine the period of the oscillation. Note added March 6: Again, make the small-angle approximation. [5] [5]