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4.1 Kinematics of Simple Harmonic Motion (SHM)

Kari Eloranta2013

Jyvskyln Lyseon lukio

International Baccalaureate

January 15, 2013

Kari Eloranta 2013 (Jyvskyln Lyseon lukio International Baccalaureate)

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4.1 Simple Harmonic Motion

Definition of Simple Harmonic Motion

In simple harmonic motion the acceleration a of the object is proportionalto the displacement x from the equilibrium position, and directed towardthe equilibrium position.

Defining Equation of Simple Harmonic Motion

The defining equation of simple harmonic motion is

a=2x (1)

where a is the acceleration of the object, and is the angular frequency of

simple harmonic motion.

Examples of simple harmonic motion include a horizontally oscillatingpendulum bob suspended from a string, and a vertically oscillating bob

suspended from a spring. Kari Eloranta 2013 (Jyvskyln Lyseon lukio International Baccalaureate)

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4.1 Simple Harmonic Motion

Definition of Period T

Period T is the time taken for one complete oscillation.

Definition of Frequency f

Frequency f is the number of oscillations per unit time.

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4.1 Simple Harmonic Motion

Frequency fThe frequency is

f=1

T(2)

where T is the period of oscillation.

The unit of frequency is

[f]=1

[T]=

1

s = 1 Hz (hertz)

For example, if the frequency of the oscillations is 10 Hz it means that10 complete oscillations take place in one second.

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Figure : A bob suspended from a string is a harmonic oscillator at small angles.

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