Glossary
Acceleration
The rate at which an object's velocity changes over time, including changes in speed or direction.
Example:
When a car speeds up from a stoplight, it experiences positive acceleration.
Amplitude
The maximum displacement or distance moved by a point on a vibrating body or wave measured from its equilibrium position.
Example:
If a swing is pulled back 3 meters from its lowest point, its amplitude is 3 meters.
Displacement
The distance and direction of an object's change in position from a reference point, often the equilibrium position in SHM.
Example:
If you push a spring 2 cm inward from its resting point, its displacement is 2 cm.
Equilibrium Position
The stable position where the net force on an object is zero, and it would remain at rest if undisturbed.
Example:
For a hanging spring with a mass, the point where the spring is at rest and not moving is its equilibrium position.
Free-Body Diagram
A diagram showing all the forces acting on a single object, represented as vectors originating from the object's center.
Example:
To analyze how a box slides down an incline, you would first draw a Free-Body Diagram showing gravity, normal force, and friction.
Frequency (f)
The number of complete cycles of an oscillation that occur per unit of time, typically measured in Hertz (Hz).
Example:
A hummingbird's wings might beat with a frequency of 80 Hz, meaning 80 beats per second.
Hooke's Law
Describes the force exerted by an ideal spring, stating that the restoring force is directly proportional to the displacement from equilibrium (F = -kx).
Example:
The behavior of a bungee cord as it stretches and pulls back can be approximated by Hooke's Law.
Ideal Springs
Theoretical springs that perfectly obey Hooke's Law, meaning their restoring force is always directly proportional to displacement and they have no mass or internal friction.
Example:
In introductory physics problems, we often assume ideal springs to simplify calculations and focus on the fundamental principles of oscillation.
Kinetic Energy
The energy an object possesses due to its motion, calculated as 1/2 * m * v^2.
Example:
A baseball thrown at high speed has significant kinetic energy.
Mass on a Spring
A system consisting of a mass attached to a spring, which, when displaced, undergoes simple harmonic motion due to the spring's restoring force.
Example:
A car's suspension system can be modeled as a mass on a spring system, absorbing shocks from the road.
Newton's Second Law
States that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass (F=ma).
Example:
When a rocket engine fires, the Newton's Second Law explains how the thrust force causes the rocket to accelerate upwards.
Pendulum
A weight suspended from a pivot so that it can swing freely, often used to demonstrate simple harmonic motion for small angles.
Example:
The swinging bob of a grandfather clock is a classic example of a pendulum.
Period (T)
The time it takes for one complete cycle of an oscillating system to occur.
Example:
If a metronome ticks back and forth once every 0.5 seconds, its period is 0.5 seconds.
Potential Energy
Stored energy an object has due to its position or configuration, such as gravitational potential energy or elastic potential energy in a spring.
Example:
A stretched rubber band stores potential energy that can be released to launch a projectile.
Restoring Force
A force that always acts to bring an object back to its equilibrium position, causing the oscillatory motion in SHM.
Example:
When you pull a rubber band, the force pulling it back to its original shape is a restoring force.
Simple Harmonic Motion (SHM)
A type of periodic motion where the restoring force is directly proportional to the displacement from the equilibrium position and acts in the opposite direction.
Example:
A mass bouncing up and down on a spring demonstrates Simple Harmonic Motion as it oscillates around its resting point.
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 very stiff car suspension spring would have a high spring constant, making the ride feel bumpy.
Velocity
The rate at which an object changes its position, including both its speed and direction.
Example:
A bird flying east at 10 m/s has a velocity of 10 m/s East.