Chapter 12 Simple Harmonic Motion tends to derive the formulas used in harmonic motion. A motion where the restoring force is directly proportional to the displacement of a body (from its mean position) is known as Simple Harmonic Motion. The direction in which this restoring force is applied is always towards the mean position. The term Harmonic or periodic motion implies that the body repeats its motion after regular intervals. Thus, a body is said to be oscillating if it is moving to and fro on the same path.
Consider a particle that is executing simple harmonic motion. Its acceleration can be given by the formula:
a(t) = -ω2 x(t). . Here, ω represents the angular velocity of the particle. The amplitude is the maximum displacement observed on either side from the centre of oscillation. Furthermore, a few terms associated with Simple harmonic motion like time period, amplitude have been discussed.
Simply put, the frequency can be defined as the inverse of the time period. Speaking physically, frequency is indicative of the number of oscillations occurring per unit time. Frequency is measured in Hertz, i.e., cycles per second.
The angular harmonic motion also is a part of harmonic motion. The angular oscillations are called angular simple harmonic motion if there is a position of the body where the resultant torque on the body is zero. This position is the mean position where θ = 0. When a body is displaced through an angle from the mean position. The time period of SHM can be expressed as
And we know,
Thus, the frequency of a simple harmonic oscillator is given by f = 1/2π* √k/m Energy takes place when a particle is in harmonic motion. The total energy of the particle participating in simple harmonic motion is constant and is independent of the instantaneous displacement.