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 mass on a spring. You’ll be focusing on describing the energy transformations, 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: Force Interactions - 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 conservation laws.

Key Concepts 

• Period (T)
• Amplitude
• Frequency (f)
• Equilibrium Point
• Kinetic Energy (K)
• Potential Energy (Ug ,Usp)

Key Equations  

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 amplitude. 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 Hooke's Law, 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 spring constant 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 spring constant.

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 1/2mv^2, 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 spring constant 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.