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Unit 6 Overview: Simple Harmonic Motion

3 min readjanuary 29, 2023

Kanya Shah

Kanya Shah

Daniella Garcia-Loos

Daniella Garcia-Loos

Kanya Shah

Kanya Shah

Daniella Garcia-Loos

Daniella Garcia-Loos

With the basics of forces and energy covered in Units 1-4, we’ll now shift our focus to applying these concepts to a new form of motion, Simple Harmonic Motion (SHM). SHM involves a periodic motion, typically focused on a pendulum or . You’ll be focusing on describing the , forces, accelerations, and velocities of these objects and discuss the practical applications of them. SHM topics will account for ~2-4% of the AP exam questions. 

Applicable Big Ideas 

Big Idea #3: - The interactions of an object with other objects can be described by forces.

Big Idea #5: Conservation - Changes that occur as a result of interactions are constrained by .

Key Concepts

  • Period (T)

  • Frequency (f)

  • Kinetic Energy (K)

  • Potential Energy (Ug ,Usp)

Key Equations  

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2Feq.PNG?alt=media&token=5e21f4ab-a2c2-4677-8a7e-f6e7428978fb

6.1 Period of Simple Harmonic Oscillators

A simple harmonic oscillator (SHO) is a system that oscillates (repeatedly moves back and forth) with a fixed frequency and . Examples of SHOs in everyday life include a swinging pendulum, a spring being stretched and released, and a mass attached to a fixed point and oscillating.

At an AP Physics 1 level, the key concept behind simple harmonic oscillators is that they follow , which states that the force acting on an object is proportional to the displacement of the object from its equilibrium position. This means that the force acting on an SHO is always directed towards its equilibrium position and is proportional to the displacement from that position.

The period of an SHO is the time it takes for the system to complete one full oscillation. The period of an SHO is dependent on the mass of the object and the of the system. The formula to calculate the period of a simple harmonic oscillator is T = 2π√(m/k) where T is the period, m is the mass and k is the .

6.2 Energy of a Simple Harmonic Oscillator

At an AP Physics 1 level, the energy of a simple harmonic oscillator (SHO) can be understood as the sum of kinetic and potential energy. The kinetic energy of an SHO is the energy an object possesses due to its motion and is equal to , where m is the mass of the object and v is its velocity. The potential energy of an SHO is the energy an object possesses due to its position and is related to the force acting on it.

In a simple harmonic oscillator, the potential energy is stored in the spring when it is stretched or compressed. The potential energy of the spring is related to the displacement x of the object from its equilibrium position by the equation:

U = 1/2kx^2

where k is the and x is the displacement of the object from its equilibrium position.

As the object oscillates, its kinetic energy will be maximum at the point of the oscillation where it is moving the fastest and its potential energy will be maximum at the point of the oscillation where it is farthest from its equilibrium position. The total energy of the simple harmonic oscillator is the sum of kinetic and potential energy which is always constant.

Key Terms to Review (17)

1/2mv^2

: This equation represents the kinetic energy (KE) of an object in motion, where m is the mass and v is the velocity. It quantifies how much energy an object possesses due to its motion.

Amplitude

: The amplitude represents the maximum displacement from equilibrium in a periodic motion.

Conservation Laws

: Conservation laws are fundamental principles in physics that state certain quantities remain constant over time, regardless of the changes happening within a system.

Energy transformations

: Energy transformations refer to processes where energy changes from one form to another.

Equilibrium Point

: The equilibrium point is the position where an object or system experiences zero net force and remains at rest or in constant motion.

Force Interactions

: Force interactions refer to the mutual action between two objects resulting from their interaction through forces. Forces always occur in pairs and act on different objects involved in an interaction.

Frequency (f)

: Frequency refers to the number of cycles or oscillations that occur in one second.

Hooke's Law

: Hooke's Law states that within the elastic limit, the force required to stretch or compress an elastic material (like a spring) is directly proportional to its displacement from equilibrium.

Key Term: U = 1/2kx^2

: Definition: The equation U = 1/2kx^2 represents the potential energy stored in a spring that is compressed or stretched. It relates the amount of potential energy (U) to the spring constant (k) and the displacement from equilibrium position (x).

Kinetic Energy (K)

: Kinetic energy is the energy possessed by an object due to its motion. It depends on the mass of the object and its velocity.

Mass on a spring

: A mass on a spring refers to a system where a mass is attached to the end of a spring and can oscillate back and forth.

Period (T)

: The period refers to the time it takes for one complete cycle of a periodic motion.

Potential Energy (Ug, Usp)

: Potential energy refers to the stored energy an object possesses due to its position or condition. It is the energy that can be converted into other forms of energy when the object's position or condition changes.

Simple Harmonic Motion (SHM)

: Simple Harmonic Motion refers to the repetitive back-and-forth motion exhibited by certain systems when they are displaced from their equilibrium position and experience a restoring force proportional to their displacement. Examples include a mass-spring system or a pendulum swinging back and forth.

Simple Harmonic Oscillator (SHO)

: A simple harmonic oscillator refers to any system that exhibits periodic motion back and forth around an equilibrium position under the influence of a restoring force proportional to its displacement from equilibrium.

Spring Constant

: The spring constant represents how stiff or flexible a spring is. It determines how much force will be required to stretch or compress a spring by a certain distance.

T = 2π√(m/k)

: This equation represents the period (T) of an object undergoing simple harmonic motion on a mass-spring system. It relates the period with the mass (m) and the stiffness of the spring (k).

Unit 6 Overview: Simple Harmonic Motion

3 min readjanuary 29, 2023

Kanya Shah

Kanya Shah

Daniella Garcia-Loos

Daniella Garcia-Loos

Kanya Shah

Kanya Shah

Daniella Garcia-Loos

Daniella Garcia-Loos

With the basics of forces and energy covered in Units 1-4, we’ll now shift our focus to applying these concepts to a new form of motion, Simple Harmonic Motion (SHM). SHM involves a periodic motion, typically focused on a pendulum or . You’ll be focusing on describing the , forces, accelerations, and velocities of these objects and discuss the practical applications of them. SHM topics will account for ~2-4% of the AP exam questions. 

Applicable Big Ideas 

Big Idea #3: - The interactions of an object with other objects can be described by forces.

Big Idea #5: Conservation - Changes that occur as a result of interactions are constrained by .

Key Concepts

  • Period (T)

  • Frequency (f)

  • Kinetic Energy (K)

  • Potential Energy (Ug ,Usp)

Key Equations  

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2Feq.PNG?alt=media&token=5e21f4ab-a2c2-4677-8a7e-f6e7428978fb

6.1 Period of Simple Harmonic Oscillators

A simple harmonic oscillator (SHO) is a system that oscillates (repeatedly moves back and forth) with a fixed frequency and . Examples of SHOs in everyday life include a swinging pendulum, a spring being stretched and released, and a mass attached to a fixed point and oscillating.

At an AP Physics 1 level, the key concept behind simple harmonic oscillators is that they follow , which states that the force acting on an object is proportional to the displacement of the object from its equilibrium position. This means that the force acting on an SHO is always directed towards its equilibrium position and is proportional to the displacement from that position.

The period of an SHO is the time it takes for the system to complete one full oscillation. The period of an SHO is dependent on the mass of the object and the of the system. The formula to calculate the period of a simple harmonic oscillator is T = 2π√(m/k) where T is the period, m is the mass and k is the .

6.2 Energy of a Simple Harmonic Oscillator

At an AP Physics 1 level, the energy of a simple harmonic oscillator (SHO) can be understood as the sum of kinetic and potential energy. The kinetic energy of an SHO is the energy an object possesses due to its motion and is equal to , where m is the mass of the object and v is its velocity. The potential energy of an SHO is the energy an object possesses due to its position and is related to the force acting on it.

In a simple harmonic oscillator, the potential energy is stored in the spring when it is stretched or compressed. The potential energy of the spring is related to the displacement x of the object from its equilibrium position by the equation:

U = 1/2kx^2

where k is the and x is the displacement of the object from its equilibrium position.

As the object oscillates, its kinetic energy will be maximum at the point of the oscillation where it is moving the fastest and its potential energy will be maximum at the point of the oscillation where it is farthest from its equilibrium position. The total energy of the simple harmonic oscillator is the sum of kinetic and potential energy which is always constant.

Key Terms to Review (17)

1/2mv^2

: This equation represents the kinetic energy (KE) of an object in motion, where m is the mass and v is the velocity. It quantifies how much energy an object possesses due to its motion.

Amplitude

: The amplitude represents the maximum displacement from equilibrium in a periodic motion.

Conservation Laws

: Conservation laws are fundamental principles in physics that state certain quantities remain constant over time, regardless of the changes happening within a system.

Energy transformations

: Energy transformations refer to processes where energy changes from one form to another.

Equilibrium Point

: The equilibrium point is the position where an object or system experiences zero net force and remains at rest or in constant motion.

Force Interactions

: Force interactions refer to the mutual action between two objects resulting from their interaction through forces. Forces always occur in pairs and act on different objects involved in an interaction.

Frequency (f)

: Frequency refers to the number of cycles or oscillations that occur in one second.

Hooke's Law

: Hooke's Law states that within the elastic limit, the force required to stretch or compress an elastic material (like a spring) is directly proportional to its displacement from equilibrium.

Key Term: U = 1/2kx^2

: Definition: The equation U = 1/2kx^2 represents the potential energy stored in a spring that is compressed or stretched. It relates the amount of potential energy (U) to the spring constant (k) and the displacement from equilibrium position (x).

Kinetic Energy (K)

: Kinetic energy is the energy possessed by an object due to its motion. It depends on the mass of the object and its velocity.

Mass on a spring

: A mass on a spring refers to a system where a mass is attached to the end of a spring and can oscillate back and forth.

Period (T)

: The period refers to the time it takes for one complete cycle of a periodic motion.

Potential Energy (Ug, Usp)

: Potential energy refers to the stored energy an object possesses due to its position or condition. It is the energy that can be converted into other forms of energy when the object's position or condition changes.

Simple Harmonic Motion (SHM)

: Simple Harmonic Motion refers to the repetitive back-and-forth motion exhibited by certain systems when they are displaced from their equilibrium position and experience a restoring force proportional to their displacement. Examples include a mass-spring system or a pendulum swinging back and forth.

Simple Harmonic Oscillator (SHO)

: A simple harmonic oscillator refers to any system that exhibits periodic motion back and forth around an equilibrium position under the influence of a restoring force proportional to its displacement from equilibrium.

Spring Constant

: The spring constant represents how stiff or flexible a spring is. It determines how much force will be required to stretch or compress a spring by a certain distance.

T = 2π√(m/k)

: This equation represents the period (T) of an object undergoing simple harmonic motion on a mass-spring system. It relates the period with the mass (m) and the stiffness of the spring (k).


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© 2024 Fiveable Inc. All rights reserved.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.