Chapter 2: Oscillation Practice Flashcards

Vocabulary practice flashcards covering periodic motion, simple harmonic motion, energy equations, and types of oscillation based on the Chapter Two lecture notes.

Periodic motion

A motion which repeats itself over and over again after a fixed interval of time, with a path that can be along any trajectory.

Oscillatory motion

A periodic motion in which a body moves back and forth, to and fro, or up and down repeatedly about a fixed mean position in a definite interval of time.

Restoring force

The force which tends to bring a body towards the mean position, defined as $F_R \times -x$ or $F_R = -kx^n$ where $n$ is any odd number.

Simple Harmonic Motion (SHM)

A special type of oscillatory motion in a straight line where acceleration is directly proportional to displacement from the equilibrium position and is always directed towards that position.

Harmonic Oscillation

The oscillation which can be expressed in terms of a single harmonic function, such as $y = A \text{sin}(\theta)$ or $y = A \text{cos}(\theta)$.

Non-harmonic Oscillation

An oscillation created by a combination of two or more than two harmonic oscillations, such as $y = A \text{sin}(\text{ω}t) + B \text{sin}(2\text{ω}t)$.

Time period (T)

The smallest time interval after which a periodic motion is repeated, or the time taken by a particle to complete one oscillation, given by $T = \frac{2\text{π}}{\text{ω}}$.

Frequency (f)

The number of oscillations or vibrations made by a body in one second, measured in hertz ($Hz$) where $f = \frac{1}{T}$.

Displacement

The distance of a particle or body from the mean position at any instant of time while executing SHM, denoted by $x$ or $y$.

Amplitude (A)

The maximum displacement of a particle or a body on either side of the mean position.

Phase

A physical quantity that completely expresses the position and direction of motion of a particle at any instant with respect to its mean position, represented by the argument $(\text{ω}t + \text{ϕ})$.

Initial phase (Epoch)

The phase of a vibrating particle at the instant $t = 0$, denoted by $\text{ϕ}$.

Velocity in SHM

The time rate of change of displacement, defined by the equation $v = \text{ω}\text{√}(A^2 - y^2)$.

Acceleration in SHM

The rate of change of velocity, defined by the equation $a = -\text{ω}^2y$, where the negative sign indicate acceleration and displacement are oppositely directed.

Potential Energy (PE) in SHM

The energy of a particle resulting from its displacement against a restoring force, calculated as $PE = \frac{1}{2}m\text{ω}^2y^2$.

Kinetic Energy (KE) in SHM

The energy a particle possesses because of its velocity, calculated as $KE = \frac{1}{2}m\text{ω}^2(A^2 - y^2)$.

Total Mechanical Energy (E)

The sum of potential and kinetic energy in SHM, which remains constant and is calculated by $E = \frac{1}{2}m\text{ω}^2A^2$.

Simple Pendulum

An ideal arrangement where a heavy point-mass is suspended by a weightless, inextensible, and perfectly flexible string from a rigid support.

Effective length

The total distance from the point of suspension to the center of gravity of the bob, calculated as the length of the thread plus the radius of the bob.

Spring constant (k)

Also known as the force constant, it represents the force required to extend or compress a spring per unit distance, given by $k = m\text{ω}^2$.

Un-damped Oscillation

An oscillation where the amplitude does not change with time and total mechanical energy remains constant due to the absence of resistive forces.

Damped oscillation

An oscillation where the amplitude decreases exponentially with time due to resistive forces like friction or viscosity, defined by the amplitude equation $R = Ae^{-\frac{bt}{2m}}$.

Damping constant (b)

A constant representing the magnitude of the damping force, which is proportional to the velocity of the oscillating body.

Free oscillation

Oscillation that occurs when a system oscillates with its own natural frequency without the help of an external periodic force.

Forced oscillation

Oscillation that occurs when a system is influenced by an external periodic driving force, causing it to oscillate at the driving frequency rather than its natural frequency.

Resonance

The phenomenon of an increase in the amplitude of oscillations when the frequency of the driving force is equal or very close to the natural frequency of the oscillator.