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Home > News & Articles > Oscillatory Motion: Definition, Types, Example, Simple Harmonic Motion (SHM) and Application
Updated on 18th May, 2023 , 7 min read
What is Oscillatory motion? In simple terms, it refers to a motion that repeats itself after a certain period. The motion can be periodic or non-periodic, and it can be linear or rotational. Oscillatory motion is a common occurrence in nature, and it is observed in many systems, including mechanical, electrical, and biological systems.
When an object moves over a point repeatedly, this is known as oscillatory motion. The ideal condition can be approached in a complete Hoover because there is no air to stop the object in oscillatory motion friction. The vibration of strings and the movement of springs are both examples of oscillatory motion in the mechanical world, and they are the same as mechanical vibration. The periodic motion should not be confused with oscillatory motion. Objects in periodic motions repeat their movement after a fixed duration or period of time, whereas objects in oscillatory motions repeat their movement over a fixed position.
There are two main types of oscillatory motion: simple harmonic motion and damped oscillations:
Simple Harmonic Motion (SHM)
Simple harmonic motion is a type of oscillatory motion where an object moves back and forth in a straight line, such that its displacement from the central point is proportional to the force acting on it. It is characterized by a constant amplitude (maximum displacement) and frequency (number of cycles per unit of time).
Some examples of simple harmonic motion include the motion of a mass attached to a spring, the motion of a pendulum, and the motion of a tuning fork.
Damped Oscillations
Damped oscillations are a type of oscillatory motion where the amplitude of the motion gradually decreases over time due to the presence of friction or other damping forces. The frequency of the motion remains constant, but the amplitude decreases until the object eventually comes to rest.
Damped oscillations can be observed in a variety of systems, such as the motion of a pendulum in a viscous fluid, the motion of a car suspension system, or the oscillations of an electrical circuit.
The equations of oscillatory motion describe the behavior of an object that is oscillating or vibrating around an equilibrium position. These equations can be used to determine the displacement, velocity, and acceleration of the oscillating object at any given time.
The basic equation of oscillatory motion is:
x(t) = A cos(ωt + φ)
Where:
Using this equation, we can calculate the velocity and acceleration of the oscillating object as follows:
Velocity:
v(t) = dx/dt = -Aω sin(ωt + φ)
Acceleration:
a(t) = d^2x/dt^2 = -Aω^2 cos(ωt + φ)
Where:
It is important to note that the displacement, velocity, and acceleration of an oscillating object are all sinusoidal functions of time. The displacement function is a cosine function, while the velocity and acceleration functions are sine and cosine functions, respectively.
The equations of oscillatory motion are widely used in various fields of science and engineering, including physics, chemistry, and mechanical engineering. They are used to describe the behavior of systems such as pendulums, springs, and electrical circuits, among others. By understanding and applying these equations, we can better understand the behavior of oscillating systems and predict their future behavior.
Oscillatory motion is a type of motion in which an object moves back and forth around a central point or position in a repetitive manner. It is a common phenomenon observed in everyday life, from the motion of a pendulum to the vibrations of a guitar string. Here are some examples of oscillatory motion:
Oscillatory motion has numerous applications in physics, engineering, and other fields. Some of the most common applications include:
The physics behind oscillatory motion can be explained using Newton's laws of motion. According to Newton's laws, an object in motion will remain in motion unless acted upon by an external force. When an external force is applied to an object, it will cause the object to accelerate. The acceleration of the object is directly proportional to the force applied.
In the case of oscillatory motion, the force applied to the object is a restoring force. A restoring force is a force that acts to bring an object back to its equilibrium position. When an object is displaced from its equilibrium position, the restoring force will cause the object to accelerate back towards its equilibrium position. This results in a repetitive motion that follows a regular pattern.
The principles of oscillatory motion describe the behavior of an object that moves back and forth repeatedly around a fixed point or equilibrium position. Here are some of the key principles of oscillatory motion:
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By - Nikita Parmar 2023-08-25 09:48:44 , 11 min readOscillatory motion is a type of motion that occurs when a system moves repeatedly back and forth around a central point, such as a pendulum swinging or a spring vibrating.
Periodic motion is a type of motion that repeats itself at regular intervals, while oscillatory motion is a type of periodic motion that involves a system moving back and forth around a central point.
The characteristics of simple harmonic motion include a restoring force that is proportional to the displacement from equilibrium, a periodic motion that is sinusoidal in nature, and a constant period and frequency.
Resonance is a phenomenon that occurs when a system is subjected to a periodic force that has the same frequency as the natural frequency of the system, resulting in a large amplitude of oscillation.
Damping is the gradual reduction in the amplitude of an oscillatory system over time due to the dissipation of energy through friction or other forms of resistance.
Underdamped oscillations occur when the damping force is less than the critical damping force, resulting in oscillations with a gradually decreasing amplitude. Overdamped oscillations occur when the damping force is greater than the critical damping force, resulting in oscillations that quickly decay to zero. Critically damped oscillations occur when the damping force is equal to the critical damping force, resulting in oscillations that quickly reach equilibrium without overshooting.
The equation for simple harmonic motion is x(t) = A cos(ωt + φ), where x is the displacement from equilibrium, A is the amplitude of oscillation, ω is the angular frequency, t is time, and φ is the initial phase angle.
The period and frequency of oscillatory motion are inversely proportional, meaning that as the frequency of oscillation increases, the period decreases, and vice versa.
The angular frequency of oscillatory motion is proportional to the square root of the spring constant divided by the mass of the system, meaning that increasing the mass or decreasing the spring constant will decrease the angular frequency.
Examples of oscillatory motion include a pendulum swinging back and forth, a mass-spring system vibrating, and the motion of sound waves.
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