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Fundamentals of Stress and Vibration 1. Mathematics for Structural mechanics
[A Practical guide for aspiring Designers / Analysts]
‘•‹†‡” ƒ †‹•–ƒ ‡ ˜• –‹‡ ‰”ƒ’Š ƒ• •Š‘™ ‹ ȏ ‹‰ ͳǤ͵Ȑ

[Fig 1.3: distance vs time]

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

‡– —• ‘•‹†‡” –Š‡ ˆ‘ŽŽ‘™‹‰ ’”‘ ‡†—”‡ǣ

‘ †‡–‡”‹‡ –Š‡ •Ž‘’‡ǡ ™‡ ‡‡† –™‘ ’‘‹–• ‘ –Š‡ —”˜‡ǡ ƒ• •Š‘™ ‹ ȏ ‹‰ ͳǤͶȐǤ ˆ –Š‡ ’‘‹–• ƒ”‡
ˆƒ” ƒ’ƒ”–ǡ –Š‡ •Ž‘’‡ ‹• ƒ˜‡”ƒ‰‡† ƒ† ‘– ƒ –—ƒŽ ƒ– –Š‡ †‡•‹”‡† ’‘‹–Ǥ Š‡ ‡””‘” ‘—Ž† „‡ •‹‰‹ϐ‹ ƒ–
†‡’‡†‹‰ ‘ –Š‡ —”˜‡ ƒ† –Š‡ ’‘‹–• Š‘•‡Ǥ

[Fig 1.4: slope of a curve]

‘•‹†‡” –Š‡ •Ž‘’‡ ‘ˆ —”˜‡ ƒ– ’‘‹– ȋ͵ȌǤ Š‡ •Ž‘’‡ ƒ– ’‘‹– ȋ͵Ȍ ‹• †‡–‡”‹‡† „› Š‘‘•‹‰ –™‘
‡ƒ”„› ’‘‹–• ȋͳȌ ƒ† ȋʹȌǤ – ‘—Ž† „‡ ‘„•‡”˜‡† ˆ”‘ ȏ ‹‰ ͳǤͶȐ –Šƒ–Ǥ –Š‡ •Ž‘’‡ ‘ˆ –Š‡ —”˜‡ ƒ– ’‘‹–•
ȋͳȌ ƒ† ȋʹȌ ‹• †‹ˆˆ‡”‡– ˆ”‘ –Š‡ •Ž‘’‡ ‘ˆ –Š‡ —”˜‡ ƒ– ’‘‹– ȋ͵ȌǤ

‡– —• ‘™ †‡–‡”‹‡ –Š‡ ’”‘š‹‹–› ‘ˆ ’‘‹–• ȋͳȌ ƒ† ȋʹȌ –‘ ‹‹‹œ‡ ‡””‘” ‹ –Š‡ †‹ˆˆ‡”‡ ‡ ‘ˆ
•Ž‘’‡•Ǥ – ‹• ‹–—‹–‹˜‡ –Šƒ– –Š‡ ‡””‘” ‹• ‹‹— ™Š‡ –Š‡ ’‘‹–• ȋͳȌ ƒ† ȋʹȌ ƒ”‡ ‹ –Š‡ Ž‘•‡•–
ƒ–Š‡ƒ–‹ ƒŽ ’”‘š‹‹–› –‘ ‡ƒ Š ‘–Š‡”Ǥ Š‹• ‡ƒ• –Šƒ–ǡ –Š‡ †‹ˆˆ‡”‡ ‡ ‹ –Š‡‹” ‹†‡’‡†‡–
‘‘”†‹ƒ–‡ ȋšȌ ‹• ˜‡”› •ƒŽŽ ƒ† ‹• –‡†‹‰ –‘ œ‡”‘Ǥ

QP No. SSC/Q4401, Version 1.0, NSQF Level 7, Compliant with Aero and Auto Industries, Page 5