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Document Title
Fundamentals of Stress and Vibration 2. Engineering Mechanics Chapter
[A Practical guide for aspiring Designers / Analysts]

It is to be observed that, the position of the bob in [Fig 2.83] is instantaneous and the tangential
velocity ‘v’ does not remain constant, rather, it is an accelerating motion.

Further, though the bob is moving away from the mean position, the acceleration is always directed
towards the mean position. This could be explained as follows:

The equation of SHM for displacement at any point is given by: y = a sin ωt

[Fig 2.84: Graph of displacement vs time]

dy y 2
2
2
2
The velocity is given by: v = = aω cosωt = aω 1 − sin ωt = aω 1 − = ω a − y
dt 2

[Fig 2.85: Graph of velocity vs time]

2
d y
2
2
And the acceleration is given by: a = = −aω sinωt = −ω y
dt 2

[Fig 2.86: Graph of Acceleration vs time]

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