Simple Harmonic Motion

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Idea spring





Hooke's Law

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

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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:

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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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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

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Elastic Deformation







Shear Deformation and the Shear Modulus








Volume Deformation and the Bulk Modulus

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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