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Simple Harmonic Motion

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Simple Harmonic Motion

Post Number: #1  Postby Jessica » October 15th, 2013, 3:19 pm

Idea spring
Image

Image


Hooke's Law
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The constant k is called the spring constant with unit N/m.

Image
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Re: Simple Harmonic Motion

Post Number: #2  Postby Jessica » October 26th, 2013, 12:04 pm

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

    Position: Image

    Velocity: Image

    Acceleration: Image



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Re: Simple Harmonic Motion

Post Number: #3  Postby Jessica » October 26th, 2013, 12:19 pm

Elastic energy
Image

Elastic potential energy
Image

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

Post Number: #4  Postby Jessica » October 31st, 2013, 3:07 pm

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:
Image (torque due to bob weight)

Image

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:
Image



Other equations
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Re: Simple Harmonic Motion

Post Number: #5  Postby Jessica » October 31st, 2013, 3:14 pm

Elastic Deformation

Image
Image




Shear Deformation and the Shear Modulus
Image

Image

Image



Volume Deformation and the Bulk Modulus
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Image

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Re: Simple Harmonic Motion

Post Number: #6  Postby Jessica » October 31st, 2013, 3:19 pm

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:
Image

SI unit: Image



Stress, Strain, and Hooke's Law

Stress and Strain Relations for Elastic Behavior
Image

Stress-strain relation
Image
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