# Elongation hourly function in the MHS

Projection of a uniform circular simple harmonic motion

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, *t _{0}* , the rover occupies position

*P*and its initial angular position is

_{0}*θ*. At a later time,

_{0}*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: