The physical pendulum. (a) In class, we derived the formula for the frequency of the physical pendulum =3 Mgl (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.

The physical pendulum. (a) In class, we derived the formula for the frequency of the physical pendulum =3 Mgl (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.

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Description: 3. The physical pendulum.(a) In class, we derived the formula for the frequency of the physical pendulumW3MglI(1)Show that the expression for the frequency of the simple pendulum is consistent withthis.Then derive (1) using the energy method, where

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Concept explainers

Simple harmonic motion

Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.

Simple Pendulum

A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.

Oscillation

In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.

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Question

3. The physical pendulum.
(a) In class, we derived the formula for the frequency of the physical pendulum
W3
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 (do/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.
=

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