IB Physics Topic C.1.1 Defining and Analyzing Simple Harmonic Motion Revision Notes (SL/HL)

IB Physics Topic C.1.1 Defining and Analyzing Simple Harmonic Motion Revision Notes (SL/HL) | RevisionDojo

Conditions for Simple Harmonic Motion (SHM)

Simple Harmonic Motion (SHM) is a special type of oscillatory motion where an object moves back and forth around an equilibrium position.

Restoring Force Proportional to Displacement

For SHM to occur, the system must have a restoring force that:
1. Acts in the opposite direction to the displacement.
2. Is directly proportional to the displacement from the equilibrium position.
This relationship can be expressed mathematically as: $$
F = -kx
$$ where:
1. $F$ is the restoring force.
2. $k$ is a constant (often called the spring constant in a spring-mass system).
3. $x$ is the displacement from the equilibrium position.

Hint

The negative sign indicates that the force acts in the opposite direction to the displacement.

Example

In a mass-spring system, when the mass is displaced to the right, the spring exerts a force to the left, trying to bring the mass back to equilibrium.
This force is proportional to how far the mass is stretched or compressed.

Acceleration in SHM

The restoring force causes the object to accelerate back towards the equilibrium position.
Using Newton’s second law, $F = ma$, we can express the acceleration as: $$
a = -\frac{k}{m}x
$$
This shows that the acceleration is also proportional to the displacement and acts in the opposite direction.

Defining Equation for SHM: $a = -\omega^2 x$

The defining equation for SHM is:

$$
a = -\omega^2 x
$$

where:

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Conditions for Simple Harmonic Motion (SHM)

Simple Harmonic Motion (SHM) is a special type of oscillatory motion where an object moves back and forth around an equilibrium position.

Restoring Force Proportional to Displacement

For SHM to occur, the system must have a restoring force that:
1. Acts in the opposite direction to the displacement.
2. Is directly proportional to the displacement from the equilibrium position.
This relationship can be expressed mathematically as: $$
F = -kx
$$ where:
1. $F$ is the restoring force.
2. $k$ is a constant (often called the spring constant in a spring-mass system).
3. $x$ is the displacement from the equilibrium position.

Hint

The negative sign indicates that the force acts in the opposite direction to the displacement.

Example

In a mass-spring system, when the mass is displaced to the right, the spring exerts a force to the left, trying to bring the mass back to equilibrium.
This force is proportional to how far the mass is stretched or compressed.

Acceleration in SHM

The restoring force causes the object to accelerate back towards the equilibrium position.
Using Newton’s second law, $F = ma$, we can express the acceleration as: $$
a = -\frac{k}{m}x
$$
This shows that the acceleration is also proportional to the displacement and acts in the opposite direction.

Defining Equation for SHM: $a = -\omega^2 x$

The defining equation for SHM is:

$$
a = -\omega^2 x
$$

where:

Definition

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Note

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Excepteur sint occaecat cupidatat non proident

Tip

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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.1.1 Defining and Analyzing Simple Harmonic Motion 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

Conditions for Simple Harmonic Motion (SHM)

Restoring Force Proportional to Displacement

Acceleration in SHM

Defining Equation for SHM: $a = -\omega^2 x$

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

Conditions for Simple Harmonic Motion (SHM)

Restoring Force Proportional to Displacement

Acceleration in SHM

Defining Equation for SHM: $a = -\omega^2 x$

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