Glossary
Acceleration due to gravity (g)
The acceleration experienced by objects falling freely near the Earth's surface, approximately 9.8 m/s². It influences the period of a simple pendulum.
Example:
On the Moon, where the Acceleration due to gravity is much lower, a pendulum clock would run significantly slower.
Acceleration due to gravity (g)
The acceleration experienced by an object due to the gravitational pull of a celestial body, typically Earth.
Example:
On the Moon, the Acceleration due to gravity is much less than on Earth, causing objects to fall slower.
Angular Frequency (ω)
A measure of the rate of change of the phase angle of an oscillation, expressed in radians per second.
Example:
For a spring-mass system, a higher Angular Frequency means the mass oscillates faster.
Displacement
The distance and direction of an object from its equilibrium position.
Example:
If a mass on a spring is pulled 5 cm from its resting point, its Displacement is 5 cm.
Equilibrium position
The position where the net force acting on an oscillating object is zero, and it would remain at rest if undisturbed.
Example:
For a hanging spring, the Equilibrium position is where the spring is at rest, neither stretched nor compressed.
Frequency (f)
The number of complete cycles or oscillations that occur per second. It is measured in Hertz (Hz), where 1 Hz equals 1 cycle per second.
Example:
A hummingbird's wings beat 80 times per second, meaning their wing beat Frequency is 80 Hz.
Frequency (f)
The number of complete oscillations or cycles that occur per unit of time, typically per second.
Example:
A speaker cone vibrating 440 times per second produces a sound with a Frequency of 440 Hz.
Inverse Relationship
A relationship between two quantities where an increase in one quantity results in a proportional decrease in the other, and vice versa. For frequency and period, this means f = 1/T.
Example:
If a metronome ticks faster (higher Frequency), the time between each tick (its Period) becomes shorter, demonstrating an Inverse Relationship.
Kinetic Energy
The energy an object possesses due to its motion.
Example:
At the equilibrium point of an SHM system, the oscillating mass has maximum Kinetic Energy.
Length (L)
The distance from the pivot point to the center of mass of the bob in a simple pendulum. It is a critical factor determining the pendulum's period.
Example:
To make a playground swing oscillate more slowly, you would need to increase the Length of its chains.
Length of the pendulum (l)
The distance from the pivot point to the center of mass of the pendulum bob.
Example:
To make a pendulum swing slower, you would need to increase the Length of the pendulum.
Mass (m)
A measure of the inertia of an object, representing the amount of matter it contains. In a spring-mass system, it directly affects the period of oscillation.
Example:
Adding more weight to a trampoline (increasing the Mass) will make it bounce slower, increasing its period of oscillation.
Mass of the bob
The mass of the object suspended at the end of a simple pendulum. Notably, for a simple pendulum, this mass does not affect its period of oscillation.
Example:
Whether you use a small pebble or a heavy rock as the Mass of the bob on a string, as long as the string length is the same, the pendulum's swing time will remain unchanged.
Object-Spring Oscillator
A system consisting of a mass attached to a spring, which oscillates back and forth when displaced from its equilibrium position. Its period depends on the mass and spring constant.
Example:
The suspension system in a car acts as an Object-Spring Oscillator, absorbing bumps as the car's mass bounces on the springs.
Oscillations
Repetitive back-and-forth or up-and-down motion about an equilibrium position.
Example:
The rhythmic swinging of a playground swing demonstrates oscillations.
Period (T)
The time it takes for one complete cycle or oscillation of a repeating motion. It is measured in seconds (s).
Example:
If a child on a swing completes one full back-and-forth motion in 3 seconds, the Period of the swing is 3 s.
Period (T)
The time it takes for one complete cycle or oscillation of a system undergoing SHM.
Example:
If a pendulum completes one full swing in 2 seconds, its Period is 2 seconds.
Potential Energy
Stored energy that an object possesses due to its position or configuration.
Example:
A stretched spring stores Potential Energy that can be converted into kinetic energy when released.
Restoring Force
The force that always acts to bring an object undergoing SHM back towards its equilibrium position.
Example:
When you stretch a rubber band, the force pulling it back to its original shape is the restoring force.
Simple Harmonic Motion (SHM)
A type of periodic motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement. It results in an oscillation that repeats over time.
Example:
A guitar string vibrating after being plucked exhibits Simple Harmonic Motion, producing a consistent musical note.
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 on a vertical spring, moving up and down rhythmically, is a classic example of Simple Harmonic Motion.
Simple Pendulum
An idealized pendulum consisting of a point mass (bob) suspended from a string of negligible mass, swinging freely under the influence of gravity. Its period depends on its length and gravity.
Example:
A grandfather clock uses a Simple Pendulum to keep accurate time, with its consistent swing determining the clock's rhythm.
Simple Pendulum
An idealized system consisting of a point mass (bob) suspended by a massless, inextensible string, swinging freely under gravity.
Example:
A grandfather clock uses a Simple Pendulum to keep accurate time.
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 Newtons per meter (N/m).
Example:
A stiffer car suspension spring would have a higher Spring Constant, making the ride feel bumpier but providing more control.
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 very stiff spring, like one in a car's suspension, would have a high Spring constant.
Spring-Mass System
A system consisting of a mass attached to a spring, which, when displaced, undergoes Simple Harmonic Motion.
Example:
Engineers might model a car's suspension as a Spring-Mass System to understand how it absorbs bumps.
Total Energy
The sum of the kinetic and potential energies in a system, which remains constant in an ideal SHM system without friction.
Example:
Even as a pendulum swings, its Total Energy (kinetic + potential) remains the same if air resistance is ignored.