Simple Harmonic Motion Examples to Know for AP Physics 1 (2025)

Simple Pendulum

A mass (bob) attached to a string or rod of fixed length.

Restoring Force in Pendulum

Component of gravitational force that brings the bob back to equilibrium.

Period of Pendulum (T)

Depends on length (L) and acceleration due to gravity (g).

Limit of SHM in Pendulum

Approximation holds for angular displacement less than 15 degrees.

Mass-Spring System

A mass attached to a spring oscillating when displaced.

Period of Mass-Spring System

Described by mass (m) and spring constant (k).

Hooke's Law

Restoring force is proportional to the displacement (x) from equilibrium.

Energy in Mass-Spring System

Oscillates between potential energy in the spring and kinetic energy of the mass.

Torsional Pendulum

A mass suspended by a wire that twists about its axis when displaced.

Period of Torsional Pendulum

Determined by moment of inertia (I) and torsional constant (κ).

Rotational Equivalent of SHM

Restoring torque proportional to angle of twist.

Vibrating String

A string fixed at both ends that vibrates to produce sound.

Nodes

Points of zero displacement in standing waves.

Antinodes

Points of maximum displacement in standing waves.

Fundamental Frequency

Depends on the string's length, tension (T), and mass per unit length (μ).

Wave Speed in String

Given by the tension (T) and mass per unit length (μ).

Oscillating Liquid in U-Tube

Liquid oscillates when displaced from its equilibrium level due to gravity.

Restoring Force in U-Tube

Generated by the height difference between liquid columns.

Vibrating Tuning Fork

Produces sound waves; frequency depends on material and shape.

Prongs of Tuning Fork

Exhibit SHM, creating consistent sound waves.

LC Circuit

Comprises an inductor and a capacitor exchanging energy between fields.

Natural Frequency of LC Circuit

Given by the inductor (L) and capacitor (C) values.

Energy in LC Circuit

Transitions between potential (electric) and kinetic (magnetic) forms.

Vertical Mass-Spring System

Mass hanging from a spring oscillates vertically.

Horizontal Mass-Spring System

Mass attached to a spring oscillates purely horizontally on frictionless surface.

Bungee Jumping

Oscillatory motion due to gravitational and elastic forces.

Interplay in Bungee Jumping

Gravitational force downward and elastic force upward.

Complex Motion in Bungee Jumping

Period varies as the cord stretches and contracts.

Applications of SHM

Includes musical instruments, engineering designs, and scientific measurements.

Insights of SHM

Analyzes and predicts behaviors across various contexts.

Connection of SHM

Links theoretical physics with practical innovations.

Base Principle of SHM

Restoring forces create periodic motion.

Real-world Examples of SHM

Pendulums, springs, tuning forks, and fluids in tubes.