Mechanics

# Speed ​​hourly function in MHS

Projection of a uniform circular simple harmonic motion

When studying oscillatory motions, we saw that simple harmonic motion consists of a common oscillatory motion and that it has great importance for Physics.

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 p , of the point P, which describes the MCU on the axis Ox .

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

How:

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