Question

Q1. Roller bearings are subject to fatigue failure caused by large contact loads. The

problem of finding the location of the maximum stress along the x axis can be shown to be

equivalent to maximizing the function:

= + x

With the aid of the secant method, use xo=0.98 and x1=0.7 to determine to within 10^-5 the

value of x that maximizes f(x).

Q 2. In an LRC series circuit, the impressed voltage E(t) and the charge q(t) on the

capacitor are related to each other by the linear second-order ordinary differential equation,

where L is the inductance, R is the resistance and C is the capacitance. Suppose we measure

the charge on the capacitor for several values of t and obtain

t	1.50	1.525	1.55	1.575	1.60
q	0.8	1.2	1.15	1.3	1.8

where t is in seconds, q is in coulombs, the inductance L is a constant 0.5h , the resistance R

is 0.3Ω and the Capacitance is 0.01 f . Approximate the voltage E(t) when t = 1.525, 1.55 and

1.575.

Answer 1