Glossary
Amplitude
The maximum displacement or distance moved by a point on a vibrating body or wave measured from its equilibrium position.
Example:
If you push a swing higher, you are increasing its amplitude, causing it to reach a greater height with each oscillation.
Closed System
A system where no matter or energy can enter or leave, ensuring that its total energy is conserved.
Example:
A perfectly sealed and insulated container of gas can be approximated as a closed system for studying its internal energy changes.
Conservation of Energy
A fundamental principle stating that the total energy of a closed system remains constant, though it can transform between different forms.
Example:
When a diver jumps from a high board, their initial potential energy is converted into kinetic energy as they fall, but the total energy of the diver-Earth system remains constant (ignoring air resistance).
Displacement from Equilibrium (x)
The distance an oscillating object is moved from its stable rest position, where the net force acting on it is zero.
Example:
When a pendulum is pulled to the side, its displacement from equilibrium is the horizontal distance from its lowest point.
Equilibrium Point
The position in an oscillating system where the net force acting on the object is zero, and it would remain at rest if undisturbed.
Example:
For a mass hanging from a spring, the equilibrium point is where the spring's upward force perfectly balances the downward force of gravity.
Internal Energy (U)
The energy associated with the random motion of a system's particles, often considered as the thermal energy within an object.
Example:
When you vigorously shake a bottle of water, the water's temperature might slightly increase due to an increase in its internal energy from the agitation.
Kinetic Energy (K)
The energy an object possesses due to its motion, directly proportional to its mass and the square of its velocity.
Example:
A fastball thrown by a pitcher has significant kinetic energy due to its high speed and mass.
Mass (m)
A fundamental property of matter that measures its inertia, or resistance to changes in motion.
Example:
A bowling ball has a greater mass than a tennis ball, which is why it's harder to accelerate or stop.
Maximum Displacement
The greatest distance an oscillating object moves from its equilibrium position during its motion, also known as the amplitude.
Example:
When a guitar string is plucked, the farthest it moves from its resting position is its maximum displacement, which determines the loudness of the sound.
Non-conservative forces
Forces, such as friction or air resistance, that cause the total mechanical energy of a system to change, often converting it into thermal energy.
Example:
When a car skids to a stop, non-conservative forces like friction between the tires and the road dissipate the car's kinetic energy as heat and sound.
Period of Oscillation
The time it takes for one complete cycle of an oscillation or wave to occur, returning to its initial state.
Example:
The period of oscillation for a child on a swing is the time it takes for them to swing forward and then back to their starting point.
Potential Energy (U)
The energy an object possesses due to its position or configuration within a force field, representing stored energy that can be converted into other forms.
Example:
A stretched rubber band stores potential energy that is released when it snaps back to its original shape.
Simple Harmonic Motion (SHM)
A type of periodic motion where the restoring force is directly proportional to the displacement from equilibrium and acts in the opposite direction.
Example:
A mass oscillating on a spring, or a pendulum swinging with small angles, are classic examples of simple harmonic motion.
Spring Constant (k)
A measure of the stiffness of a spring, indicating the amount of force required to stretch or compress it by a unit distance.
Example:
A stiffer spring, like those found in heavy-duty truck suspensions, will have a much larger spring constant than a soft toy spring.
Total Energy
The sum of all forms of energy within a system, which remains constant in the absence of external non-conservative forces.
Example:
In a frictionless roller coaster ride, the total energy of the car is the constant sum of its kinetic and gravitational potential energy at any point on the track.
Velocity (v)
The rate at which an object changes its position, specifying both its speed and direction of motion.
Example:
A car traveling at 60 mph north has a different velocity than a car traveling at 60 mph east, even though their speeds are the same.