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 a swing goes 2 meters forward from its lowest point, its amplitude is 2 meters.
Angular Frequency (ω)
The rate of oscillation or rotation expressed in radians per second, related to frequency and period.
Example:
For a mass-spring system, a higher angular frequency means the mass oscillates back and forth more rapidly.
Frequency (f)
The number of complete cycles of an oscillation or wave that occur per unit of time.
Example:
A speaker cone vibrating 440 times per second produces a sound with a frequency of 440 Hz.
Kinetic Energy (KE)
The energy an object possesses due to its motion.
Example:
At the equilibrium position of a mass-spring system, the oscillating mass has its maximum kinetic energy.
Mass-Spring Systems
A system consisting of a mass attached to a spring, which, when displaced, oscillates in simple harmonic motion.
Example:
The suspension of a car, where the car body acts as the mass and the shock absorbers contain springs, is a practical mass-spring system.
Oscillations
The back-and-forth movement of an object around its equilibrium position.
Example:
A guitar string vibrating after being plucked demonstrates rapid oscillations.
Period (T)
The time required for one complete cycle of an oscillation or wave to occur.
Example:
If a pendulum completes one full swing (back and forth) in 2 seconds, its period is 2 seconds.
Phase Angle (φ)
An initial angle that determines the starting position or state of an oscillating system at time t=0.
Example:
If an oscillation starts at its maximum positive displacement, its phase angle would typically be 0 or 2π radians.
Potential Energy (PE)
Stored energy an object possesses due to its position or configuration.
Example:
When a spring is fully compressed or stretched, the system has its maximum elastic potential energy.
Resonance
A phenomenon where an oscillating system experiences a large increase in amplitude when an external force is applied at its natural frequency.
Example:
Pushing a child on a swing at just the right time (its natural frequency) causes the swing's amplitude to increase due to resonance.
Restoring Force
A force that always acts to pull or push an object back towards its equilibrium position.
Example:
When you stretch a rubber band, the elastic force pulling it back to its original shape is a restoring force.
Simple Harmonic Motion (SHM)
A special type of periodic motion where the restoring force is directly proportional to displacement and acts in the opposite direction, resulting in sinusoidal motion.
Example:
A perfectly frictionless mass on a spring, bobbing up and down, exhibits ideal Simple Harmonic Motion.
Simple Pendulums
A system consisting of a point mass (bob) suspended from a string or rod of negligible mass, swinging freely under gravity.
Example:
A grandfather clock uses a simple pendulum to keep accurate time through its regular oscillations.
Spring Constant (k)
A measure of the stiffness of a spring, indicating how much force is required to stretch or compress it by a certain distance.
Example:
A car's suspension system uses springs with a high spring constant to support the vehicle's weight and absorb shocks.
Total Mechanical Energy (E)
The sum of the kinetic and potential energies in a system, which remains constant in the absence of non-conservative forces like friction.
Example:
In an ideal mass-spring system, the total mechanical energy is conserved, constantly transforming between kinetic and potential forms.