Mechanics

# Elongation hourly function in the MHS

Projection of a uniform circular simple harmonic motion

Simple harmonic motion is a common oscillatory motion of great relevance in Physics. It is a periodic movement in which symmetrical displacements occur around a point.

In order to obtain the hourly function of the elongation, without using superior calculation resources, it is possible to use a device that consists of analyzing the projection of a uniform circular motion on one of its diameters. The movement of this projection is an MHS.

Elongation hourly function in the MHS

Let’s consider the rover in the figure above describing an MCU of period T , on the circle with center O and radius A. At the initial instant, 0 , the rover occupies position 0 and its initial angular position is θ 0 . At a later time, t , the mobile starts to occupy position P , associated with the angular position θ .

Based on the MCU study we can say that:

As R = A and , then:

Elongation hourly function in the MHS

In it, θ0 is called the initial phase of the MHS and is measured in radians. The quantity ω is called the angular frequency of the MHS and is expressed in radians per second (rad/s). Note that the angular frequency corresponds to the angular velocity of the MCU and has the same relationship with the period already studied in the MCU:

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