Question

Bachelor of Engineering Technology (Civil) Program School of Engineering, Design and Construction ENGINEERING MATHEMATICS 2 (BET 203) Assignment-: Differential equations Answer all questions showing your work very clearly Attach completed Assignment cover sheot Please note that class participation is compulsory for this Assessment Duc date: 2A 2019 (6.00 pm) late submissions will incur 10% of penalty each day it is late. All work produced must be neat and clear. Word processed is preferred. 1. The cantilever beam AB of length L shown in Fig.(a) carries a uniformly distributed load of intensity wo, which includes the weight of the beam. Equation of the elastic curve is given by the following differential equatiorn M- -- where M is the bending moment of the beam. It is also given that where E- Modulus of the elasticity of the beam and I modulus of Inertia. v is the deflection of the beam Compute the maximum displacement of the beam using L- 2.5 m, wo 500 kg/m, and E 2.1x10 pa. 2. According to Newton's Law of Universal Gravitation, the gravitational force on an object of mass m that has been projected vertically upward from Earth's surface 1s hee x x(t) is the object's distance above the surface at time t, R is Earth's radius, (x+R) and g is the acceleration due to gravity. Also, by Newton's Second law, dy F=ma = mat--(x+R)2 a. Suppose a rocket is fired vertically upward with an initial velocity vo . Let h be the maximunm height above the surfaced reached by the object. Show that 2gRh 27,- civ (hint: mmv) b. Calculate ve limvo This limit is called escape velocity for Earth. Use R-6.4 x 106 m and g = 9.8 m/s to calculate ve ln m/s. c. 3. Find the solutions of the following initial value problems a a e +x(1)-2 b2xt.x(1)-4

Answer 1

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