## Testing convergence of a sample Logarithmic series using Leibnitz’s rule

Below is the solution to test convergence of a sample Logarithmic series –

## Finding maximum power transmitted neglecting centrifugal tension

Below is a sample problem and its solution to find maximum power transmitted in a scenario where we need to neglect centrifugal tension.

## Finding power transmitted by a belt given max tension

Below is the solution to find power transmitted by a belt given maximum permissible tension and rpm of a larger pulley –

## Finding maximum power transmitted from maximum belt stress

Here is a problem involving V-belt where we calculate the maximum power transmitted from the maximum belt stress and other attributes in the system –

## Finding Velocity and maximum power transmitted

Here is an interesting solution to find velocity and maximum power transmitted –

## Finding Torque and power transmitted

Here is an interesting problem and solution to calculate torque and power transmitted of a shaft and pulley system. You can easily extend this to larger systems.

## Finding maximum power transmitted and initial tension

Its interesting to use the mechanical formulas to find maximum power transmitted and initial tension given the characteristic features of a flat belt pulley system. Below is an example problem and its solution –

## Finding power transmitted by a pulley

Here is a real life mechanical problem to solve – Two parallel shafts whose center lines are 4.8m apart are connected on an open belt drive. The diameter of the larger pullet is 1.5m and that of the smaller pulley is 1.05m. The initial tension in the belt when stationary is 3KN. The mass of…

## Finding maximum cross sectional area of a Mechanical belt

Question: A leather belt transmits 30 KW from a pulley 750 mm diameter which runs at 500 rpm. The belt is in contact with the pullry over an arc of 160° and coefficient of friction, μ = 0.3. If the permissible stress in the belt is not to exceed 2 MN / m^2, find the maximum…

## Finding Tight side and Slack side tension of a mechanical belt

Question: An electric motor provides 6.6 KW to a belt driven pulley 125 mm in diameter. The speed of the pulley is 1050 rpm. Calculate the tight side and slack side tension of the belt if they are in the ratio 7:2? Ans: Given: Power, P = 6.6KW Diameter, d = 125×10^-3m Speed of the pulley,…

## Discussing Convergence of Iteration and Newton Raphson Methods

We use various Numerical methods to solve algebraic and transcendental equations. All these methods converge the result to a single root after various approximations specific to each method. In this article we delve into details of rate of convergence of two popular methods – Iterative and Newton Raphson method. Enjoy!

## Solving Equations by Jacobi’s Iteration Method

Jacobi’s Iteration method is an interesting method to solve equations by simple iteration method. Here is an example –

## Solving a set of equations using Gauss Seidal Elimination Method

Here is an excellent example of Gauss Seidal elimination method to solve a set of equations –

## Finding Inverse of a Matrix using Gauss Elimination Method

Here is an intelligent and simple way to find the inverse of a matrix using Gauss Elimination method –

## Gauss Jordan Elimination Method

Here is a well explained solution to solve a set of equations using Gauss Jordan Elimination method –

## Gauss Elimination Method

Below is a well explained solution for a set of equations using Gauss Elimination method. Enjoy!

## Finding Roots of equation x3-3×2+x+1=0

We will be using Newton Raphson method to find the root of this equation. Enjoy!

## Parallel Lamp Connection

Below is the lab work for Parallel Lamp Connection –

## Dim and Bright Connection

Here is the detailed lab work for a Dim and Bright lamp connection –

## Master Electric Connection

We will see how to operate 3 lamps using a master switch and also simultaneously operating them.

## Fluorescent Tube connection

Below is a simple step by step description of a Fluorescent Tube connection. We will see the list of materials needed, the procedure to build it observation and result.

## Finding measure of skewness and kurtosis for Poisson distribution

Here we define what Poisson Distribution is how to measure its skewness and kurtosis.

## Proving Inversion Mapping

Here we venture to prove that Inversion Mapping maps the totality of circles lines in the Z plane on to the same that of W plane –

## Find 4th Root of 1 and Square root of -8i

Here is an interesting solution to find nth root of a complex number Z. Here we use a general equation to find the 4th root of 1 and square of -8i. Enjoy!

## Finding Linear Fractional Transformation

Ok, here is a beautiful mathematical solution to find the Linear Fractional Transformation which maps |Z| <= 1 on to |W| <=1 such that Z = i/4 is mapped onto W=0. Also we will graph out the images of the lines x=c and y=c.

## Transformation of W=eZ

Here we discuss transformation of W = eZ

## Forming a Bi-Linear Transformation which maps a set of points

Here is a mathematical solution for forming a Bi-Linear Transformation which maps the points (1, i,-1) onto the points  (i,0,-i) and hence finding the image of |Z| < 1 and also finding the Invarient points of this Transformation 🙂

## How to determine which mathematical functions are analytic

Here is the solution on how to determine if a mathematical function is analytic –

## Mathematical solution for checking a certain function satisfy Laplace Equation

Here is an attempt to check if a function satisfies Laplace Equation and determining corresponding analytical function –

## Locus of a point Z satisfying condition |Z-1| + |Z+1| = 4

Here is a fun solution for Mathematics students to find the locus of a point Z satisfying condition |Z-1| + |Z+1| = 4 –