Page 88 - Singiresu S. Rao-Mechanical Vibrations in SI Units, Global Edition-Pearson (2017)

1.10 harmoniC motion 85
mean position, is known as simple harmonic motion. The motion given by x = A cos vt
is another example of a simple harmonic motion. Figure 1.46 clearly shows the similarity
between cyclic (harmonic) motion and sinusoidal motion.
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1.10.1 Harmonic motion can be represented conveniently by means of a vector OP of magnitude
Vectorial A rotating at a constant angular velocity v. In Fig. 1.47, the projection of the tip of the vec-
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representation tor X = OP on the vertical axis is given by
of harmonic y = A sin vt (1.33)
motion and its projection on the horizontal axis by

x = A cos vt (1.34)

u vt

3p

2p
A

One
cycle p
of motion

P
x
O

x A cos vt
y

P
A P A
v y A sin vt Angular
displacement
O u vt O p 2p 3p u vt

One cycle of motion

FiGure 1.47 Harmonic motion as the projection of the end of a rotating vector.