Shock response spectrum (SRS): Foundations — Hinglish deep dive

3.6.13 · D1 · Physics › Spacecraft Structures & Systems Engineering › Shock response spectrum (SRS)

Yeh page har us symbol ko build karta hai jo parent note mein aata hai, ek aisi bachche se shuru karke jisne kabhi spring, integral, ya Greek letter nahi dekha. Ise upar se neeche padho — har idea woh floor hai jis par agla idea khada hai.

1. Sab kuch ke peeche ki tasveer: ek mass on a spring

Kisi bhi symbol se pehle, woh machine dekho jis par poora topic based hai.

Figure dekho. Ek block (component — ek circuit board, ek bracket) ek spring aur ek dashpot (ek piston jo jab tum ise tezi se hilao toh pushback deta hai) par baitha hai. Spring ka nichla sira base — spacecraft ki wall — se juda hua hai. Jab spacecraft ko kick lagti hai, base hilta hai, spring khichti hai, aur block jhoomta hai.

Yahan se kyun shuru? Kyunki ek real spacecraft mein laakhon jhoomte hue parts hote hain, lekin kisi bhi ek resonance ke paas har part is ek simple ghanti ki tarah behave karta hai (yeh Modal analysis ka vaada hai). Ek ghanti master kar lo, aur tum sabko describe kar sakte ho.

2. Position, aur uske upar sawaar do cheezein

Neeche sab kuch us block ki ek upar-neeche line ke saath measure kiya gaya hai.

Parent note mein yeh upar dots ke saath likhe hain. Ek dot ka matlab hai "rate of change of," Newton se liya hua.

Hume specifically acceleration kyun chahiye? Kyunki acceleration hi cheezein todti hai. Ek kamre mein dheeray khisak jaane se koi nahi tuta; slam kiya jaana (badi acceleration) ek solder joint tod deta hai. Poora SRS peak acceleration isliye measure karta hai. Dekho Acceleration response in structures.

3. Base motion vs. relative motion — sabse mushkil tasveer

Yeh woh confusion hai jo zyaadatar beginners ko dooba deta hai. Ek saath do motions ho rahi hain.

Base hilta hai (spacecraft ki wall jhatka deti hai). Iske acceleration ko $a (t)$ kaho — woh shock jo hume di gayi hai.
Block bhi hilta hai, spring ke zariye khicha hua.
Spring jo actually feel karta hai woh unke beech ka farq hai: block base se kitna peechhe reh gaya.

4. Greek letters: ghanti ki personality ka naam

Har ghanti ki ek pitch aur ek ring-time hoti hai. Do Greek letters unhe capture karte hain.

Ek hi cheez ke do versions kyun? $f_{n}$ insanon ke liye friendly hai ("yeh board 200 Hz par ring karta hai"). $ω_{n}$ equations ke liye friendly hai, kyunki circles aur springs ki maths radians mein baat karti hai. Woh ek hi fact hai do costumes mein.

Figure mein teen blocks pluck karke release kiye gaye hain: ek barely damped (lamba ring), ek moderate, ek heavily. Envelope — woh fading dotted line — $ζ$ set karta hai; wiggle rate $ω_{n}$ set karta hai.

5. Woh ingredients jo $ω_{n}$ aur $ζ$ banate hain

Pitch aur ring-time kahan se aate hain? Block-spring-damper ki teen physical properties se.

Yeh teeno personality letters mein combine ho jaate hain:

$ω_{n}$ mein square root kyun? Kyunki restoring push stretch ke saath badhti hai jabki sluggishness mass ke saath badhti hai, aur wiggle-rate unke ratio ke square root par depend karti hai — wahi maths jo pendulum ka period $L / g$ par depend karta hai. Tum ise yahan prove nahi karna; bas shape par trust karo: pitch $\propto k / m$ .

6. Woh law jo block ko govern karta hai: $F = ma$ disguise mein

Ab pieces ko parent ke central equation mein assemble karo.

Newton kehta hai: (mass)(acceleration) = (forces ka sum). Hamare block par, forces hain spring pull, damper drag, aur shaking base se inertial kick.

Term by term, words mein:

$\overset{z}{¨}$ — block ki apni jiggle-acceleration.
$2 ζ ω_{n} \overset{z}{˙}$ — damper speed se lad raha hai.
$ω_{n}^{2} z$ — spring stretch se lad raha hai.
$- a (t)$ — base ka kick, opposite direction mein push ke roop mein feel hota hai (accelerating car mein "seat mein dhakel jaane" ka feeling). Force-vs-motion view ke liye dekho Mechanical impedance.

Yeh ek line kyun matter karta hai? Kyunki agar tum ise solve kar sako — kisi diye gaye kick $a (t)$ se $z (t)$ nikaalo — tum block ki slamming compute kar sakte ho, aur isliye uska SRS.

7. Woh tools jo ise solve karte hain: sine, exponential, integral

Parent ka solution (Duhamel's integral) teen maths tools use karta hai. Inhe seedha taur par samjho.

8. Ek ghanti se poore spectrum tak

Ek ghanti (ek $f_{n}$ ) ek number deti hai: uski worst slam.

Prerequisite map

Equipment checklist

Apne aap ko test karo — right side cover karo aur zor se jawab do.

Ek symbol ke upar ek dot ka kya matlab hai?

Rate of change per second — agar symbol ek position hai toh velocity.

Do dots ka kya matlab hai?

Rate of change ki rate of change — ek acceleration.

Relative displacement

z

kya hai?

Block position minus base position — block apne base se kitna offset hai; yahi spring ko khichta hai.

Absolute acceleration

a_{abs}

kya hai?

Block ki total acceleration ground se dekhi hui, base acceleration

a (t)

plus block ka apna

\overset{z}{¨}

; yahi parts ko damage karta hai.

ω_{n}

f_{n}

mein convert karo.

ω_{n} = 2 π f_{n}

— radians per second versus puri wiggles per second.

ζ = 0.05

physically kya matlab hai?

5% damping — ring moderately fade hoti hai; equivalently

Q = 10

ω_{n} = k / m

mein square root kyun hai?

Pitch stiffness aur mass ke ratio par depend karta hai, aur woh ratio square root ke neeche enter karta hai — stiffer/lighter matlab higher pitch.

Solution mein exponential

e^{- ζ ω_{n} t}

kya karta hai?

Yeh woh fading envelope hai jo ring ko time ke saath shrink karta hai.

Integral

\int_{0}^{t} d τ

kya accomplish karta hai?

Yeh har tiny past push ka bacha hua ring add karta hai, shuru se ab tak.

Ek sentence mein, SRS kya hai?

Har ghanti ki single worst acceleration ka curve, ghanti ki natural frequency ke against plot kiya hua.

1 g

kya hai?

Earth ki gravity ki acceleration, lagbhag

9.81

m/s².

Recall Self-check: kya tum machine draw kar sakte ho?

Block-spring-damper ko ek moving base par sketch karo, $z$ ko us gap ke roop mein label karo jo spring feel karta hai, aur $a (t)$ ko base kick ke roop mein mark karo. Agar tum yeh memory se kar sako, tum parent note ke liye taiyaar ho.