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## Simple Harmonic Motion

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### Simple Harmonic Motion

Idea spring

Hooke's Law

The constant k is called the spring constant with unit N/m.

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### Re: Simple Harmonic Motion

Simple Harmonic Motion: The oscillatory motion that results when an elastic material is subjected to the restoring force of an ideal spring.

Position:

Velocity:

Acceleration:

$\omega = \sqrt{\frac{k}{m}}$

$T = 2\pi\sqrt{\frac{m}{k}}$
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### Re: Simple Harmonic Motion

Elastic energy

Elastic potential energy

Total mechanical energy

Total mechanical energy is conserved if no work is done by non-conservative forces
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### Re: Simple Harmonic Motion

The Pendulum
A simple pendulum consists of a particle of mass m, attached to a frictionless pivot P by a cable of length L and negligible mass.

For small displacement of the pendulum:
(torque due to bob weight)

Since the mass of the string is much smaller than that of the bob, all the mass is practically at the bob, which is like a point mass at a distance L from the pivot point. In this case, the moment of inertia is just I = mL2. So:

Other equations

$L = \frac{T^2g}{4\pi^2}$
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### Re: Simple Harmonic Motion

Elastic Deformation

Shear Deformation and the Shear Modulus

Volume Deformation and the Bulk Modulus

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### Re: Simple Harmonic Motion

Pressure
The pressure P is the magnitude F of the force acting perpendicular to a surface divided by the area A over which the force acts:

SI unit:

Stress, Strain, and Hooke's Law

Stress and Strain Relations for Elastic Behavior

Stress-strain relation
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