Glossary
Amplitude
The maximum displacement or distance moved by a point on a vibrating body or wave measured from its equilibrium position.
Example:
If a speaker cone vibrates 2 mm back and forth, its amplitude is 2 mm.
Circular Motion
The motion of an object along the circumference of a circle or rotation along a circular path.
Example:
The blades of a spinning fan exhibit circular motion.
Displacement (x)
The distance and direction of an object from its equilibrium position.
Example:
If a pendulum bob swings 10 cm to the right from its lowest point, its displacement is +10 cm.
Displacement (x)
The distance and direction of an object from its equilibrium position.
Example:
If a pendulum is pulled 10 cm to the side from its lowest point, its displacement is 10 cm.
Energy Conservation
The principle that the total mechanical energy (sum of kinetic and potential energy) of a system remains constant if only conservative forces are doing work.
Example:
In a frictionless roller coaster, the sum of its kinetic and potential energy at any point demonstrates energy conservation.
Energy Conservation (in SHM)
The principle that the total mechanical energy (kinetic + potential) of a system undergoing SHM remains constant if no non-conservative forces are present.
Example:
As a mass on a spring oscillates, its kinetic energy is maximum when potential energy is zero, and vice-versa, demonstrating energy conservation.
Equilibrium Position
The position where the net force acting on an object is zero, resulting in zero acceleration.
Example:
A swing hanging motionless at the bottom of its arc is at its equilibrium position.
Equilibrium Position
The point where the net force on an object is zero, and if at rest, the object would remain at rest.
Example:
For a hanging spring with a mass, the point where the mass hangs motionless is its equilibrium position.
Frequency (f)
The number of complete oscillations or cycles that occur per unit of time.
Example:
A tuning fork vibrating 440 times per second has a frequency of 440 Hz.
Frequency (f)
The number of complete cycles of periodic motion that occur per unit of time, measured in Hertz (Hz). It is the reciprocal of the period (f = 1/T).
Example:
A speaker cone vibrating 440 times per second has a frequency of 440 Hz.
Hooke's Law
A principle stating that the force needed to extend or compress a spring by some distance is proportional to that distance, expressed as F = -kx.
Example:
If you hang a 1 kg mass on a spring and it stretches 0.05 m, you can use Hooke's Law to find the spring's stiffness.
Mass on a Spring
A system consisting of a mass attached to a spring, commonly used to demonstrate Simple Harmonic Motion.
Example:
A toy car bouncing up and down on its suspension after hitting a bump can be modeled as a mass on a spring system.
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 thrust force causes the rocket to accelerate according to Newton's Second Law.
Pendulum
A mass suspended from a pivot, free to swing back and forth under the influence of gravity.
Example:
The swinging weight in a grandfather clock is a pendulum, regulating the clock's timekeeping.
Period (T)
The time taken for one complete oscillation or cycle of a periodic motion.
Example:
If a child on a swing completes one full back-and-forth motion in 3 seconds, the period of the swing is 3 seconds.
Period (T)
The time it takes for an object undergoing periodic motion to complete one full cycle of its motion.
Example:
If a swing takes 2 seconds to go back and forth once, its period is 2 seconds.
Periodic Motion
Any motion that repeats itself at regular intervals over a consistent path.
Example:
The Earth's orbit around the Sun is a form of periodic motion, completing a cycle approximately every 365 days.
Periodic Motion
Any motion that repeats in a regular cycle over a consistent period of time.
Example:
The consistent swing of a grandfather clock's pendulum is an example of periodic motion.
Restoring Force
A force that always acts to bring an object back towards its equilibrium position.
Example:
When you stretch a rubber band, the force pulling it back to its original shape is a restoring force.
Restoring Force
A force that always acts to bring an object back towards its equilibrium position, opposing the displacement.
Example:
When you stretch a rubber band, the force pulling it back to its original shape is a restoring force.
Restoring Torque
A rotational force that acts to bring a rotating object back to its equilibrium angular position.
Example:
When you twist a torsion bar, the restoring torque tries to untwist it and return it to its original state.
Simple Harmonic Motion (SHM)
A specific type of periodic motion where the restoring force is directly proportional to the displacement from equilibrium and acts in the opposite direction.
Example:
A guitar string vibrating after being plucked exhibits Simple Harmonic Motion, producing a consistent musical note.
Simple Harmonic Motion (SHM)
A special 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, where its motion is SHM because the spring's force always pulls it back towards the center.
Small Angle Approximation
An approximation used for pendulums where the sine of a small angle is considered approximately equal to the angle itself in radians, allowing the motion to be treated as SHM.
Example:
To accurately calculate the period of a playground swing using the SHM formula, you must assume its maximum swing angle is small, applying the small angle approximation.
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. It is measured in N/m.
Example:
A stiff car suspension spring would have a high spring constant, meaning it resists compression strongly.
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 unit distance.
Example:
A car's suspension system uses springs with a high spring constant to absorb bumps effectively.