Period, Frequency and Angular Frequency | CAIE 9702 Paper 4 Notes

Chapters

Paper 4

Physics9702

Period, Frequency and Angular Frequency

Timing an oscillation can be described as seconds per cycle, cycles per second or radians per second.

One cycle: period, frequency and angular frequency

One complete oscillation must return to the same position and the same direction of motion. Moving from one extreme to the other is only half a cycle.

Definition

1 mark

What is meant by the period of an oscillation?

Model answer: The time taken for one complete oscillation.

Definition

1 mark

What is meant by the frequency of an oscillation?

Model answer: The number of complete oscillations per unit time.

Definition

1 mark

What is meant by the angular frequency of an oscillation?

Model answer: The rate of change of phase of the oscillation.

f=\dfrac{1}{T}

Symbols

$f$ = frequency (Hz)
$T$ = period (s)

\omega=2\pi f

Symbols

$\omega$ = angular frequency (rad s⁻¹)
$f$ = frequency (Hz)

\omega=\dfrac{2\pi}{T}

Symbols

$\omega$ = angular frequency (rad s⁻¹)
$T$ = period (s)

Worked example

Turn a count into the three frequencies

A mass completes 24 oscillations in 6.0 s. Find its frequency, period and angular frequency.

Divide the number of cycles by the total time.
$f=\dfrac{24}{6.0}=4.0\ \mathrm{Hz}$
Take the reciprocal.
$T=\dfrac{1}{4.0}=0.25\ \mathrm{s}$
Convert cycles per second into radians per second.
$\omega=2\pi(4.0)=25\ \mathrm{rad\,s^{-1}}$

Answer

f=4.0\ \mathrm{Hz},\quad T=0.25\ \mathrm{s},\quad \omega=25\ \mathrm{rad\,s^{-1}}

Your turnquick check

An oscillator completes 15 cycles in 12 s. Find its frequency, period and angular frequency.

Show worked answer

f=\dfrac{15}{12}=1.25\ \mathrm{Hz}

T=\dfrac{1}{1.25}=0.80\ \mathrm{s}

\omega=2\pi(1.25)=7.85\ \mathrm{rad\,s^{-1}}

Period, Frequency and Angular Frequency

Timing an oscillation can be described as seconds per cycle, cycles per second or radians per second.

One cycle: period, frequency and angular frequency

One complete oscillation must return to the same position and the same direction of motion. Moving from one extreme to the other is only half a cycle.

Definition

1 mark

What is meant by the period of an oscillation?

Model answer: The time taken for one complete oscillation.

Definition

1 mark

What is meant by the frequency of an oscillation?

Model answer: The number of complete oscillations per unit time.

Definition

1 mark

What is meant by the angular frequency of an oscillation?

Model answer: The rate of change of phase of the oscillation.

f=\dfrac{1}{T}

Symbols

$f$ = frequency (Hz)
$T$ = period (s)

\omega=2\pi f

Symbols

$\omega$ = angular frequency (rad s⁻¹)
$f$ = frequency (Hz)

\omega=\dfrac{2\pi}{T}

Symbols

$\omega$ = angular frequency (rad s⁻¹)
$T$ = period (s)

Worked example

Turn a count into the three frequencies

A mass completes 24 oscillations in 6.0 s. Find its frequency, period and angular frequency.

Divide the number of cycles by the total time.
$f=\dfrac{24}{6.0}=4.0\ \mathrm{Hz}$
Take the reciprocal.
$T=\dfrac{1}{4.0}=0.25\ \mathrm{s}$
Convert cycles per second into radians per second.
$\omega=2\pi(4.0)=25\ \mathrm{rad\,s^{-1}}$

Answer

f=4.0\ \mathrm{Hz},\quad T=0.25\ \mathrm{s},\quad \omega=25\ \mathrm{rad\,s^{-1}}

Your turnquick check

An oscillator completes 15 cycles in 12 s. Find its frequency, period and angular frequency.

Show worked answer

f=\dfrac{15}{12}=1.25\ \mathrm{Hz}

T=\dfrac{1}{1.25}=0.80\ \mathrm{s}

\omega=2\pi(1.25)=7.85\ \mathrm{rad\,s^{-1}}