Page 87 - Singiresu S. Rao-Mechanical Vibrations in SI Units, Global Edition-Pearson (2017)

84 Chapter 1 Fundamentals oF Vibration

k
x(t)

A
m
S
x
O
p 2p 3p u vt

A

R
Slotted rod

P

A x A sin vt
O u vt

FiGure 1.46 Scotch yoke mechanism.

This motion is shown by the sinusoidal curve in Fig. 1.46. The velocity of the mass m at
time t is given by

dx
= vA cos vt (1.31)
dt
and the acceleration by
2
d x
2
2
= -v A sin vt = -v x (1.32)
dt 2
It can be seen that the acceleration is directly proportional to the displacement. Such a
vibration, with the acceleration proportional to the displacement and directed toward the