Determine the damping factor ratio using Secant method.

in Word Problem Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

The Secant Method is similar to Newton’s Method, but, instead of using calculus to find gradients, it calculates gradients (slopes) on a finite basis, that is, taking two points close to one another and estimating the gradient between them.

In this problem let’s replace omega/p with the variable x.

Let f(x)=2-1/√([1-x²]²+4(0.1221)²x²).

The slope between two points (x₀,f(x₀)) and (x₁,f(x₁)) is:


So the Secant Method to find x₂ is:



A graph shows that there are two positive roots to f(x)=0. We use initial guesses close to these roots to apply the Secant Method.

The tables below show the initial values as x=0.5 and 1.2, and successive iterations using an x increment of 0.1.


More to follow... (see comment)

by Top Rated User (816k points)
reshown by

x'=x+0.1. This is part of the mechanism for calculating the slope. An arbitrary increment of x (0.1) has been applied to find the slope at (x',f(x')).


∆x=f(x')/slope. Next x = f(x')-∆x.

Summary x=0.72997, 1.18639.

Related questions

Welcome to, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
86,022 questions
91,946 answers
23,906 users