# Speed hourly function in MHS

Projection of a uniform circular simple harmonic motion

Without using superior calculation resources, to obtain the hourly speed function, a device can be used that consists of analyzing the projection of a uniform circular motion on one of its diameters. The motion of this projection is an MHS, which is a periodic motion in which symmetrical displacements take place around a fixed point.

**Speed hourly function in MHS**

Let’s assume that the scalar velocity of the point ** Q** , describing the MHS, is defined by projecting the velocity

**, of the point**

*v*_{p}**which describes the MCU on the axis**

*P,***.**

*Ox*From the right triangle highlighted in the figure above, we have:

How:

*v _{p} = ω.R, R=A and θ= θ _{0} +ω.t*

Then,

**v(t)=-ω.A.sen (θ _{0} +ω.t)**

Time function of speed in the MHS

The negative sign in the above equation was placed because the velocity v has a direction opposite to the axis *Ox*