Recent content by coverband

Thank you. I neglected the tension on the hanging weight in it’s free body diagram

The weight accelerating/pulling the trolley is changed and corresponding acceleration recorded. What I don’t understand is why the weight added/removed to the hanging weight is removed/added to the trolley

No because when deriving an equation for v we start with a = dv/dt -> dv = a dt -> v=[int]a dt -> v = u + at. This is how Wikipedia derives the first equation of motion. They treat a as a constant. Thanks for your first answer though

speed = distance/time v=s/t Acceleration = dv/dt = -s/t^2 ?

Homework Statement \frac{d^2y}{dx^2} + (y^4-1)\frac{dy}{dx} = 0 Homework Equations \frac{dy}{dx} + (y^4-1) = 0 The Attempt at a Solution \frac{dy}{dx} = (1- y^4) \frac{dy}{1- y^4} = dx Then I get a horrible expression involving logs and inverse tan functions...

Ok. Let's call it an ODE: \frac{d^2y}{dx^2} + (y^4-1)\frac{dy}{dx} = 0 Now how solve please !

How do you solve with s.o.v. ?

Homework Statement \frac{\partial^2X}{\partial a^2} + (X^4-1)\frac{\partial X}{\partial a} = 0 Homework Equations How do I go about solving this PDE ? The Attempt at a Solution Please help !

There was a mistake in what I originally posted. The PDE to be solved is simpler: \frac{\partial^2X}{\partial a^2} + (X^4-1)\frac{\partial X}{\partial a} = 0 Would really appreciate your input. Thanks

Homework Statement 2\frac{\partial^2X}{\partial a \partial b} + \frac{\partial X}{\partial a}(x^4-1) = 0 Homework Equations How do I go about solving this PDE ?? The Attempt at a Solution Please help !

Homework Statement (asinz + bsin3z)^3 = (3a/4)(a^2 – ab + 2b^2)sinz – (1/4)(a^3 – 6a^2 – 3b^3)sin3z... Homework Equations The Attempt at a Solution How is this so !? What is being used here (taylor/binomial...?)

Homework Statement \frac{d^2x}{dt^2}-x-ax^2+bx^3=0 Homework Equations Please help me start this. I've never seen a d.e. with ax^2+bx^3 The Attempt at a Solution I think it ends as a fourier. Not sure. Please help me start!

Thanks The integral is \int_{0}^{2\pi} a^2(sint)^3H(-asint)dt Help !?

How would you integrate product of heaviside function and function of x i.e. int[f(x)H(x)dx] Thanks

Homework Statement The relationship between velocity and position of a simple pendulum is given by the equation y= \pm\sqrt(2(C+\omega^2 cos x)). The corresponding phase diagram is attached. How on Earth did they come up with the phase diagram. How do you plot such a complicated equation...