Glossary
Amplitude (A)
The maximum displacement or distance moved by a point on a vibrating body or wave measured from its equilibrium position.
Example:
If you pull a spring 10 cm from its resting position, the amplitude of the resulting oscillation is 10 cm.
Conservation of Energy
A fundamental principle stating that the total energy of an isolated system remains constant over time, though it may transform from one form to another.
Example:
In a closed system, even as a ball rolls down a ramp, its conservation of energy means that the sum of its kinetic and potential energy stays the same.
Elastic Potential Energy
Potential energy stored as a result of the deformation of an elastic object, such as the stretching or compressing of a spring.
Example:
When you pull back the string of a bow, you store elastic potential energy in the bow, ready to launch an arrow.
Elastic Potential Energy
The specific type of potential energy stored in a deformable elastic object, such as a spring, when it is stretched or compressed from its equilibrium position.
Example:
When you compress a spring in a toy dart gun, you are storing elastic potential energy in it.
Energy Conservation
The principle stating that the total energy of an isolated system remains constant over time, though it may transform between different forms.
Example:
When a roller coaster goes down a hill, its gravitational potential energy converts into kinetic energy, but the total mechanical energy, ignoring friction, remains conserved.
Equilibrium Position
The position where the net force on an oscillating object is zero, and it would remain at rest if undisturbed.
Example:
For a spring-mass system hanging vertically, the equilibrium position is where the spring's upward force balances gravity.
Equilibrium Position
The point in an oscillating system where the net force acting on the object is zero. At this point, the oscillating object has maximum velocity and thus maximum kinetic energy.
Example:
For a mass hanging from a spring, the equilibrium position is where the spring's upward force balances the gravitational force.
Extreme Positions
The points in an oscillation where the displacement from equilibrium is maximum, and the velocity of the oscillating object is momentarily zero.
Example:
For a pendulum, the extreme positions are the highest points it reaches on either side of its swing.
Force-Displacement Relationship
Describes how the restoring force in an oscillating system depends on the object's displacement from its equilibrium position.
Example:
In a spring, the force-displacement relationship is linear, meaning a larger stretch results in a proportionally larger restoring force.
Kinetic Energy
The energy an object possesses due to its motion, which depends on its mass and velocity. It is at its maximum when the object passes through the equilibrium position.
Example:
A roller coaster car speeding down a hill has significant kinetic energy.
Kinetic Energy (K)
The energy an object possesses due to its motion, calculated as half the product of its mass and the square of its velocity.
Example:
A fast-moving baseball has a lot of kinetic energy due to its speed.
Maximum Displacement (Amplitude)
The greatest distance or extent to which an oscillating object moves from its equilibrium position. At this point, the object's velocity is zero, and its potential energy is at its maximum.
Example:
If a swing goes 2 meters from its lowest point, its maximum displacement (or amplitude) is 2 meters.
Maximum Kinetic Energy
The highest kinetic energy achieved by an oscillating object, occurring at the equilibrium position where its velocity is greatest.
Example:
A swing reaches its maximum kinetic energy as it passes through the lowest point of its arc.
Maximum Potential Energy
The highest potential energy stored in an oscillating system, occurring at the extreme positions where displacement is greatest and velocity is zero.
Example:
A trampoline jumper has maximum potential energy at the peak of their jump, just before falling.
Periodic Motion
Any motion that repeats itself in a regular cycle over a fixed period of time.
Example:
The Earth's orbit around the Sun is an example of periodic motion.
Potential Energy
Stored energy an object possesses due to its position or configuration, which can be converted into kinetic energy. In SHM, it is maximum at the points of maximum displacement.
Example:
A stretched rubber band holds potential energy that can be released to launch a projectile.
Potential Energy (U)
Stored energy an object possesses due to its position or configuration, which can be converted into kinetic energy.
Example:
A stretched rubber band stores potential energy that can be released to launch a paper airplane.
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, like a bouncing toy on a spring, demonstrates Simple Harmonic Motion.
Simple Harmonic Motion (SHM)
A type of periodic motion where the restoring force is directly proportional to the displacement from an equilibrium position and acts in the opposite direction. This results in an oscillation about that equilibrium point.
Example:
A mass attached to a spring oscillating back and forth on a frictionless surface demonstrates Simple Harmonic Motion.
Spring Constant
A measure of the stiffness of a spring, representing the force required to stretch or compress the spring by a unit distance. It is denoted by 'k' and is crucial for calculating elastic potential energy.
Example:
A stiff car suspension spring would have a high spring constant, meaning it resists deformation strongly.
Spring Constant (k)
A measure of the stiffness of a spring, representing the force required to stretch or compress the spring by a unit distance.
Example:
A stiff car suspension spring would have a high spring constant, meaning it's hard to compress.
Total Energy
In a system undergoing SHM, the total mechanical energy is the constant sum of its kinetic energy and potential energy throughout the oscillation.
Example:
For a pendulum swinging, the total energy at any point is the sum of its kinetic energy and gravitational potential energy, always remaining the same.
Total Energy (E_total)
The sum of all forms of energy within a system, which remains constant in an isolated system undergoing Simple Harmonic Motion.
Example:
In a swinging pendulum, the sum of its kinetic and potential energy at any point is its total energy, which stays the same.