Recent content by SafiBTA

Thanks! I read through your link on the vertical spring mass. I understand that: - When the mass is hanging vertically, the spring is stretched but not "fully stretched". - Vertical spring mass system can still be assumed as horizontal spring mass system. - The displacement variable in the...

If I include the GPE, I get: U_spring = ½ k (4 r θ)² U_gravity = m g (r θ) So the total potential energy is: U = 8 k r² θ² + m g r θ Now include the kinetic energy: T = ½ (m r² + J₀) θ̇² Now apply conservation of energy: d/dt (T + U) = 0 Therefore the equation of motion is: (m r² +...

As I understand, there will be an mgx term that will turn into mg after differentiation

I’m looking at the attached vibration problem. The solution in the manual includes the spring potential energy but does NOT include the gravitational potential energy of the hanging mass. Can someone explain why gravitational potential energy is not included when deriving the equation of...

Homework Statement In writing the definition of ##e## i.e. ##e=\displaystyle\lim_{n\rightarrow\infty}(1+\frac{1}{n})^n##, why do we denote the variable by 'n' despite the fact that the formula holds for n∈(-∞,∞)? Is there any specific reason behind this notation i.e. does the variable have...

Homework Statement I need to confirm if I correct in saying the following: If f(x) is a function having the domain [a,b) as shown in the figure, then f(x) has several local maxima but none of them is global maximum, and f(x) does not have a global maximum. Homework Equations and...

Homework Statement Let A be a set of critical points of the function f(x). Let B be a set of roots of the equation f''(x)=0. Let C be a set of points where f''(x) does not exist. It follows that B∪C=D is a set of potential inflection points of f(x). Q 1: Can there exist any inflection points...

Some calculators say (-2)2/3 is equal to ##-\frac{1}{2^\frac{1}{3}}+i\frac{3^\frac{1}{2}}{2^\frac{1}{3}}## while others say its equal to ##4^{\frac{1}{3}}## i.e. ##|-\frac{1}{2^\frac{1}{3}}+i\frac{3^\frac{1}{2}}{2^\frac{1}{3}}|##. I think I am right to imply from above that (-2)2/3 does have an...

Infinitesimal difference :DD.

- This may be a stupid question as I am totally new to the concept of interest. I don't even know if my question is valid. - Figure is given below for referenceSuppose I deposit some money in a bank that pays compound interest on yearly basis. If I decide to withdraw my amount at the end of 3.5...

You can work towards a 1 year intensive diploma - http://diploma.ictp.it/application-admission/diploma-programme .

Stephen Wolfram (creator of Wolfram Mathematica) earned a PhD in theoretical physics before he completed his undergraduate. He had taught himself physics and was publishing papers at a very young age (13 as far as I remember [look it up!]). In college, he combined some of his papers into his PhD...

##Δ## is what matters to me.

You can't really understand elementary particle behavior when your brain limited to classical mechanics. Please upgrade your brain to a quantum version :smile: You can start here: https://www.bulletproofexec.com/bulletproof-upgraded-brain-octane/ Considering the particle-wave duality theory...