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2:59
YouTube
Maths By Dr Shruti
📘 Laplace Transform | Main Formula Explained (Quick Concept)
In this vIn this video, we understand the main formula of Laplace Transform in a simple and clear way. 🔥 Perfect for beginners and quick revision! 👉 Covers: Definition of Laplace Transform Mathematical formula explanation Basic idea of time domain to s-domain 💡 Learn the core concept in just a few minutes. #LaplaceTransform # ...
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🔥 Day 117 — Can you solve this? Evaluate the integral (a > 0, b ≥ 0): ∫₀^∞ e^(−a x) · sin(bx) / x dx It looks tough — but a parameter derivative makes it collapse 📉 Differentiate with respect to b, use the Laplace transform of cos(bx), then integrate back. 👉 Hint: F′(b) = ∫₀^∞ e^(−a x) cos(bx) dx = a/(a² b²). Integrate in b and use F(0) = 0 to nail the constant 👀 Would you land the exact expression before time runs out? ⏱️ 💭 Drop your answer below 👇 ✅ Full step-by-step solution is already
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Let’s find the transfer function for this translational mechanical system. Here, we have a mass-spring-damper system. It is clear that the input is the force 𝑓(𝑡) and the output is the displacement 𝑥(𝑡). The restoring force of the Hookean spring, along with the viscous damping force, impede the motion brought about by the forcing function 𝑓(𝑡). By drawing a free-body force diagram, we can use Newton’s Second Law to set up a second-order differential equation which formulates a dynamic mode
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