steel cable of length S is suspended as shown in t. The maximum tensile stress in the cable, which occurs at the support, is???????? = ??????????????where,?? = ???? ??????????= tensile stress in the...

steel cable of length S is suspended as shown in t. The maximum tensile stress in the cable, which occurs at the support, is???????? = ??????????????where,?? = ???? ??????????= tensile stress in the cable at O?? = weight of the cable per unit volume?? = horizontal span of the cableThe length to span ratio of the cable is related to ?? by ?? = ??????????????Find ???????? if ??= 77 kN/m3, ??=1000 m, and ??= 1100 m (error= 0.01%).


NUMERICAL ANALYSIS Assignment # 1 2021-2022 ______________________________________________________________________________ Q1: The displacement of structure ( ? ) is defined by the following equation for a damped oscillation: ? = 8?−?? cos ?? where k = 0.5 and ω = 3. (i): Use the graphical method to make an initial estimate of the time (t) required for the displacement to decrease to 4. (ii): Use the Newton-Raphson method to determine the time (t) to 0.01% error. ------------------------------------------- Q2: A steel cable of length S is suspended as shown in t. The maximum tensile stress in the cable, which occurs at the support, is ???? = ??????? where, ? = ?? ??? ??= tensile stress in the cable at O ? = weight of the cable per unit volume ? = horizontal span of the cable The length to span ratio of the cable is related to ? by ? ? = ????? ? Find ???? if ?= 77 kN/m 3, ?=1000 m, and ?= 1100 m (error= 0.01%). ------------------------------------------------------- Q3: Derive the two-equation form of the Newton-Raphson method. ---------------------------------------------------------- Q4: Use Newton's method to approximate solutions to the following nonlinear system. Start with x = (0.1, 0.1, -0. 1). Set the tolerance to be 10-5.