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Oscillation is a repetitive and periodic change with respect to time. It is measured with respect to some reference or central value. Mechanical oscillation is called vibration. Real examples of oscillation are AC (alternating current), pendulum, and heartbeat.
Oscillations can create waves. Some waves are visible, some are not. The unit used for the number of oscillations per second is hertz. It is defined by quantities such as amplitude, frequency, and time period.
Properties of oscillations
Frequency: It is defined as the number of oscillations per unit of time.
Amplitude: It is defined as the maximum displacement from its central position.
Time period: It is defined as the time taken for complete oscillations in unit time.
The relation between time period and frequency is given by f = 1/T
There are several types of oscillations such as simple harmonic, damped and driven oscillations, coupled oscillations. In this article, we will study, in brief, about damped oscillation.
An oscillator is a semiconductor device which produces oscillations similar to sinusoidal waves.
Types of oscillations
Damped oscillation
A damped oscillation means its amplitude decreases gradually, i.e., the oscillation fades away with time. There are some mechanisms by which an oscillator loses energy such as friction and radiation. For example, tuning a fork produces sound waves resulting in reducing energy.
Due to friction and radiation present in a circuit, amplitudes of oscillations decrease with time. Thus, a reduction in amplitude or energy of an oscillator is called damping and this type of oscillation is called damped oscillation. Damping reduces the oscillation frequency. There are two types of damping: natural damping and artificial damping.
The damping ratio is defined as how the oscillations decay due to a disturbance. It is represented by £(zeta). It is a dimensionless quantity.
Examples are a weight on spring, swinging pendulum, and RLC (resistor-inductor-capacitor) circuit.
In an RLC series circuit, at t = 0, the time capacitor gets discharged through the resistor and inductor. In this condition, the equation of current and voltage is given by:
I(t) = Vo e-at sin(Bt)
BL
V(t) = Vo e-at cos(Bt)
Where,
B = √1 R2
LC 4L2
a = R/2L
V = initial voltage
C = capacitance (farads)
R = resistance (ohms)
L = inductance (henrys)
E = base of natural log
The above current equation is for a damped sinusoidal wave. It represents a sine wave of maximum amplitude (V/BL) multiplied by a damping factor of exponential decay. As a result, we get a waveform of oscillations bounded by a decaying envelope (gradually decreasing).
From the above equations, we can classify damped oscillations into three types. If we simplify under a root term, then it is R2C2-4LC.
Types of damped oscillation
Overdamped oscillation
When the R2C2-4LC term is positive and a and B are positive numbers, oscillations are overdamped. In this case, the circuit does not show any oscillation.
Overdamped systems move towards equilibrium conditions more slowly compared to critically damped systems.
For an overdamped system, the value of zeta £>1.
Underdamped oscillation
When the R2C2-4LC term is negative and a and B are imaginary numbers, oscillations are underdamped. In this case, the circuit shows an exponentially decreasing sinusoidal waveform. An underdamped system oscillates through an equilibrium position. For an underdamped system, the value of zeta<1.
An example is mass oscillating in the spring.
Critically damped oscillation
When the R2C2-4LC term is zero, then A and B are also zero, So, oscillations are called critically damped. In this case, the circuit shows an exponentially decreasing narrow peak signal.
Value of zeta for critically damped oscillation £=1
Critical damping is the most desired situation because, in this case, the system rapidly comes into equilibrium condition. Also, the force applied to the critically damped system moves the system to a new, stable equilibrium condition without undergoing an overshoot stage.
An example of a critically damped system is the shock absorbers in a car. It is advantageous to have the oscillations decay as fast as possible. Here, the system does not oscillate, but approaches the equilibrium condition as quickly as possible.
Undamped oscillations
Simple harmonic motion, which is consistent at infinity without loss of energy or amplitude, is called undamped or free oscillations.
For an undamped system, the value of zeta £=0
Free oscillation
The oscillation of the body with natural frequency does not require any external force to initiate motion. This is called free oscillation.
It does not undergo damping. However, in practice, damping is observed until we apply external force to overcome damping. In this type of system, the amplitude, frequency, and energy remain constant. However, in ideal conditions, every object undergoes external changes resulting in the loss of energy. The frequency depends on the nature and structure of the oscillating body.
Examples of free oscillation include the motion of a simple pendulum in vacuum, the pushing of a swing just once, the sound of a musical instrument, tuning fork. The natural frequency that swings require to oscillate is called resonant frequency.
Forced oscillation
Forced oscillation refers to the oscillation of a body with external force to initiate motion. The externally applied force is called the driving force.
In this case, the amplitude undergoes damping. However, its amplitude remains constant when external energy is applied to the system. This type of oscillation does not have natural frequency; it requires an external force.
The amplitude of an object varies; it may increase, decrease, or remain constant depending upon the driving force, resistive force, and other parameters.
Example: When we apply force to someone on a swing, we have to apply force periodically so that its speed is not reduced.
Conclusion
There are different types of oscillations in which their parameters of response depend upon the application of external force. In forced oscillation, the parameters change on the application of an external force, while in free oscillation, all the parameters remain constant.
In damped oscillation, forces, such as friction and air resistance, remove energy from the oscillator. As a result, system response amplitude starts to decrease gradually with time. There are different types of damped oscillations in which, depending upon the value of damping ratio, their responses change respectively. Thus, reduction in amplitude is due to energy loss in the system due to external forces.
Conclusion
The measure of temperature is the microscopic kinetic energy of molecules and atoms that is able to transfer to neighbouring molecules and atoms in a process known as heat conduction. The rate of heat conduction varies for different objects and materials. We define a heat conduction equation as one that describes the heat flow for a body of material of known dimension and placed under a temperature difference. The coefficient of thermal conductivity is a constant that appears in this equation. Its value describes how easily heat transfer can take place for different materials. Furthermore, we discussed the applications of thermal conductivities in describing thermal conductors and insulators.
