Testing convergence of a sample Logarithmic series using Leibnitz’s rule
Below is the solution to test convergence of a sample Logarithmic series –
Below is the solution to test convergence of a sample Logarithmic series –
Below is a sample problem and its solution to find maximum power transmitted in a scenario where we need to neglect centrifugal tension.
Below is the solution to find power transmitted by a belt given maximum permissible tension and rpm of a larger pulley –
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 –
Here is an interesting solution to find velocity and maximum 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.
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 –
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…
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…
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,…
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!
Jacobi’s Iteration method is an interesting method to solve equations by simple iteration method. Here is an example –
Here is an excellent example of Gauss Seidal elimination method to solve a set of equations –
Here is an intelligent and simple way to find the inverse of a matrix using Gauss Elimination method –
Here is a well explained solution to solve a set of equations using Gauss Jordan Elimination method –
Below is a well explained solution for a set of equations using Gauss Elimination method. Enjoy!
We will be using Newton Raphson method to find the root of this equation. Enjoy!
Below is the lab work for Parallel Lamp Connection –
Here is the detailed lab work for a Dim and Bright lamp connection –
We will see how to operate 3 lamps using a master switch and also simultaneously operating them.
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.
Here we define what Poisson Distribution is how to measure its skewness and kurtosis.
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 –
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!
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.
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 🙂
Here is the solution on how to determine if a mathematical function is analytic –
Here is an attempt to check if a function satisfies Laplace Equation and determining corresponding analytical function –
Here is a fun solution for Mathematics students to find the locus of a point Z satisfying condition |Z-1| + |Z+1| = 4 –