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

Spring Potential Energy: this is given by:

work done = Spring Force ∗ average displacement

This is because, the spring force is growing linearly with displacement.

x 1
2
work done = kx ∗ s = kx ∗ = kx
avg
2 2

[Fig 2.5: work done by a spring force (F) over a stretch (x)]

šƒ’Ž‡ǣ ƒ ’‘‹– ƒ•• ‹• ”‡Ž‡ƒ•‡† ˆ”‘ ƒ Š‡‹‰Š– ȋ Ȍ ƒ• •Š‘™ ‹ ȏ ‹‰ ʹǤ͸ȐǤ ‹† –Š‡ ‘’”‡••‹‘
‹ –Š‡ •’”‹‰ǡ ƒ••—‹‰ ƒ ‹‹–‹ƒŽ ‘†‹–‹‘ –Šƒ–ǡ –Š‡ •’”‹‰ ‹• ‹ ‹–• ƒ–—”ƒŽ Ž‡‰–ŠǤ

‘Ž—–‹‘ǣ –Š‹• ’”‘„Ž‡ ‹• „ƒ•‡† ‘ –Š‡ ’”‹ ‹’Ž‡ ‘ˆ ‡‡”‰› ƒ† ™‘” ”‡Žƒ–‹‘Ǥ ‹–‹ƒŽŽ›ǡ –Š‡ ’‘‹–
ƒ••ǡ Šƒ• –‘–ƒŽ ‰”ƒ˜‹–ƒ–‹‘ƒŽ ’‘–‡–‹ƒŽ ‡‡”‰›ǡ ƒ ’ƒ”– ‘ˆ ™Š‹ Š ‹• •’‡– ƒ‰ƒ‹•– ˆ”‹ –‹‘Ǥ Š‡
”‡ƒ‹‹‰ ‹• ‘˜‡”–‡† –‘ ‰”ƒ˜‹–ƒ–‹‘ƒŽ ’‘–‡–‹ƒŽ ‡‡”‰› ƒ† ‡Žƒ•–‹ •’”‹‰ ‡‡”‰›Ǥ
‡– —• †‡˜‡Ž‘’ ƒ ‡š’”‡••‹‘ ˆ‘” Š‡‹‰Š– ȋ Ȍ –Šƒ– ƒŽŽ‘™• ‡”–ƒ‹ •’”‹‰ ‘’”‡••‹‘Ǥ

[Fig 2.6: a point mass negotiating an inclined track]

Page 12 QP No. SSC/Q4401, Version 1.0, NSQF Level 7, Compliant with Aero and Auto Industries,