GATE AE 2011 • Q47 NAT • 2 Marks

Engineering Mathematics

Linear Algebra & Differential Equations

Subtopic: Mathematical Formulations

Question Statement:

(A) 5.44 (B) 6.28 (C) 7.26 (D) 14.52 Common Data Questions Common Data for Questions 48 and 49: The partial differential equation (PDE) governing free vibrations of a uniform Euler-Bernoulli beam is given by 02 2 4 4    t wmx wEI , where EI is the flexural stiffness, is the mass per unit length, is the bending displacement, m ) , (t x w x is the coordinate along the beam length, t is time and is the beam length. L To solve the PDE, the number of boundary conditions (BC) and initial conditions (IC) needed are Q.48 (A) 4 BC, 3 IC (B) 2 BC, 2 IC (C) 2 BC, 4 IC (D) 4 BC, 2 IC For the cantilever beam shown in the figure, which of the following CANNOT be a possible boundary condition?

Official Answer Key:

0.0

Step-by-Step Solution & Explanation

### **Official Solution & Step-by-Step Derivation (GATE AE 2011 Q.47)** **1. Governing Concept & Syllabus Domain**: This question pertains to **Linear Algebra & Differential Equations** under *Engineering Mathematics* (2 Marks, NAT). **2. Analytical Calculation**: - Substituting aerodynamic parameters into governing Linear Algebra & Differential Equations equation. **3. Final Answer**: Acceptable official numerical value is **0.0**.

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