** Amplitude vs Frequency
**

Amplitude and frequency are two of the basic properties of periodic motions. A proper understanding in these concepts is required in the study of motions such as simple harmonic motions and damped harmonic motions. In this article, we are going to discuss what frequency and amplitude are, their definitions, the measurement and dependencies of amplitude and frequency, and finally the difference between amplitude and frequency.

**Frequency**

Frequency is a concept discussed in periodic motions of objects. To understand the concept of frequency, a proper understanding of periodic motions is required. A periodic motion can be considered as any motion that repeats itself in a fixed time period. A planet revolving around the sun is a periodic motion. A satellite orbiting around the earth is a periodic motion even the motion of a balance ball set is a periodic motion. Most of the periodic motions we encounter are circular, linear or semi-circular. A periodic motion has a frequency. The frequency means how “frequent” the event is. For simplicity, we take frequency as the occurrences per second. Periodic motions can either be uniform or non-uniform. A uniform can have a uniform angular velocity. Functions such as amplitude modulation can have double periods. They are periodic functions encapsulated in other periodic functions. The inverse of the frequency of the periodic motion gives the time for a period. Simple harmonic motions and damped harmonic motions are also periodic motions. Thereby the frequency of a periodic motion can also be obtained using the time difference between two similar occurrences. The frequency of a simple pendulum only depends on the length of the pendulum and the gravitational acceleration for small oscillations.

**Amplitude**

Amplitude is also a very important property of a periodic motion. To understand the concept of amplitude, the properties of harmonic motions must be understood. A simple harmonic motion is a motion such that the relationship between the displacement and the velocity takes the form of a = -ω^{2}x where “a” is the acceleration and “x” is the displacement. The acceleration and the displacement are antiparallel. This means the net force on the object is also on the direction of the acceleration. This relationship describes a motion where the object is oscillating about a central point. It can be seen that when the displacement is zero the net force on the object is also zero. This is the equilibrium point of the oscillation. The maximum displacement of the object from the equilibrium point is known as the amplitude of the oscillation. The amplitude of a simple harmonic oscillation strictly depends on the total mechanical energy of the system. For a simple spring – mass system, if the total internal energy is E, amplitude is equal to 2E/k, where k is the spring constant of the spring. At that amplitude, the instantaneous velocity is zero; thereby, the kinetic energy is also zero. Total energy of the system is in the form of potential energy. At the equilibrium point, the potential energy becomes zero.

• Amplitude strictly depends on the total energy of the system, whereas frequency of an oscillation depends on the properties of the oscillator itself. • For a given system, the amplitude can be changed but frequency cannot. |

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