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 v p , of the point P, which describes the MCU on the axis 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
