IB Physics Topic C.1.2 Time Period of Oscillatory Systems Revision Notes (SL/HL)

IB Physics Topic C.1.2 Time Period of Oscillatory Systems Revision Notes (SL/HL) | RevisionDojo

Written by official IB examiners

Period of Oscillations in a Mass-Spring System

In a mass-spring system, a mass $ m $ is attached to a spring with a spring constant $ k $.
When the mass is displaced from its equilibrium position and released, it oscillates back and forth.
The period of these oscillations is given by:

$$
T = 2\pi \sqrt{\frac{m}{k}}
$$

Tip

When solving for the period $T$, ensure that the spring constant $k$ is in $\text{N m}^{-1}$ and the mass $m$ is in $\text{kg}$ for consistent SI units.

Derivation of the Formula

Restoring force: The spring exerts a force proportional to the displacement $ x $, described by Hooke’s Law: $$ F = -kx $$
Newton’s Second Law: The force causes an acceleration $ a $, so $$ ma = -kx $$
Acceleration in SHM: In simple harmonic motion, $ a = -\omega^2 x $, where $ \omega $ is the angular frequency.
Equating the two expressions: $$
ma = -kx \implies a = -\frac{k}{m}x
$$
Angular frequency: Comparing with $ a = -\omega^2 x $, we find $$ \omega^2 = \frac{k}{m} $$
Period: The period $ T $ is related to angular frequency by $ T = \frac{2\pi}{\omega} $, so: $$
T = 2\pi \sqrt{\frac{m}{k}}
$$

Nice try, unfortunately this paywall isn't as easy to bypass as you think. Want to help devleop the site? Join the team at https://revisiondojo.com/join-us. exercitation voluptate cillum ullamco excepteur sint officia do tempor Lorem irure minim Lorem elit id voluptate reprehenderit voluptate laboris in nostrud qui non Lorem nostrud laborum culpa sit occaecat reprehenderit

Definition

Paywall

(on a website) an arrangement whereby access is restricted to users who have paid to subscribe to the site.

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Lorem ipsum dolor sit amet, consectetur adipiscing elit. Sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

Duis aute irure dolor in reprehenderit

Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.

Note

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam quis nostrud exercitation.

Excepteur sint occaecat cupidatat non proident

Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit aut fugit, sed quia consequuntur magni dolores eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci velit.

Tip

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.
Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris.
Duis aute irure dolor in reprehenderit in voluptate velit esse cillum.

Unlock the rest of this chapter with a free account

Period of Oscillations in a Mass-Spring System

In a mass-spring system, a mass $ m $ is attached to a spring with a spring constant $ k $.
When the mass is displaced from its equilibrium position and released, it oscillates back and forth.
The period of these oscillations is given by:

$$
T = 2\pi \sqrt{\frac{m}{k}}
$$

Tip

When solving for the period $T$, ensure that the spring constant $k$ is in $\text{N m}^{-1}$ and the mass $m$ is in $\text{kg}$ for consistent SI units.

Derivation of the Formula

Restoring force: The spring exerts a force proportional to the displacement $ x $, described by Hooke’s Law: $$ F = -kx $$
Newton’s Second Law: The force causes an acceleration $ a $, so $$ ma = -kx $$
Acceleration in SHM: In simple harmonic motion, $ a = -\omega^2 x $, where $ \omega $ is the angular frequency.
Equating the two expressions: $$
ma = -kx \implies a = -\frac{k}{m}x
$$
Angular frequency: Comparing with $ a = -\omega^2 x $, we find $$ \omega^2 = \frac{k}{m} $$
Period: The period $ T $ is related to angular frequency by $ T = \frac{2\pi}{\omega} $, so: $$
T = 2\pi \sqrt{\frac{m}{k}}
$$

Definition

Paywall

(on a website) an arrangement whereby access is restricted to users who have paid to subscribe to the site.

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Note

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam quis nostrud exercitation.

Excepteur sint occaecat cupidatat non proident

Tip

Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.
Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris.
Duis aute irure dolor in reprehenderit in voluptate velit esse cillum.

Topic A - Space, time and motion5 subtopics

Topic B - The particulate nature of matter5 subtopics

Topic C - Wave behaviour5 subtopics

Topic D - Fields4 subtopics

Topic E - Nuclear and quantum physics5 subtopics

IB Physics C.1.2 Time Period of Oscillatory Systems Notes

Topic A - Space, time and motion5 subtopics

Topic B - The particulate nature of matter5 subtopics

Topic C - Wave behaviour5 subtopics

Topic D - Fields4 subtopics

Topic E - Nuclear and quantum physics5 subtopics

Period of Oscillations in a Mass-Spring System

Derivation of the Formula

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Excepteur sint occaecat cupidatat non proident

Unlock the rest of this chapter with a free account

Period of Oscillations in a Mass-Spring System

Derivation of the Formula

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Excepteur sint occaecat cupidatat non proident

Unlock the rest of this chapter with a free account