Q5 A The Length Of A Part Of A Cable Of A Suspension Bridge Can Be Found By Integrating The Term 1 Twx 2 0 5 Where 1 (59.33 KiB) Viewed 83 times
Q5. a) The length of a part of a cable of a suspension bridge can be found by integrating the term [1+(Twx)2]0.5 where w is a load per unit length, T is tension and x is a distance along the Bridge. Use the binomial expansion to expand expression up to and include x8. (10 marks) b) The head loss h in a pipe is given by h=2gDCLV2 where C is constant, L is the pipe length, V is the mean velocity of fluid, D is diameter of the pipe and g is acceleration due to gravity. If the error in measuring L,V and D is +0.1%,+1.5% and +1% respectively, find the approximate percentage error in h. (15 marks) [Total 25 marks] Q6. a) The current, i through a series RL circuit id given by Ldtdi+Ri=t Show that, if t=0,i=0, then i=Rt+R2L(e−LRt−1) (9 marks) b) Solve each of the following differential equations i) dx2d2y+3dxdy−10y=0 ii) dx2d2y+4y=0
ii) dx2d2y+4dxdy+4y=0 (2 mat c) By applying Newton's second law to a body of mass m at a distance x the following differential equation is obtained dt2d2x+9x=−18 Find the general solution when x=0,dtdx=0 at t=0. -THE END- (10 [Tota
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