If a function s(t) exists, does a function t(s) always exist?
Are there functions with no inverse relationships?
Suppose
s = \int^t_a e^{u^2} du
Can there be a t(s)?
I wouldn't worry too much about C++. Take chem.
C++ is not a standard language in the physics community. In fact, the standard language completely changes based on your research interests. In undergrad you should only expect a primer in coding that prepares you to learn a new language as...
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I now study...
Yes, it's on the ground.
Right, the work done on the object should be zero about a closed path. Regardless of the fact that my work is not zero.
The work done on this chain will certainly be zero about any closed path.
The change in mass does not matter.
Then I suppose my force is...
Homework Statement
You are lifting a chain straight up at a constant velocity v_0. The chain has a linear mass density λ. What is the force required to lift the chain as a function of height?
The Attempt at a Solution
U = mgh = λygh
The height in the potential energy is the same as...
And, if you're quick, you can also roll under a moving train between its wheels.
Leidenfrost will save you when you spill a bit on your hands. Doing anything else is not safe.
Liquid nitrogen safety sprint:
don't put your hands in it. Not even for a second.
Point it away from you when you turn it on.
Sometimes gloves are more dangerous than bare hands! Just be wise.
Nitrogen, in large quantities, can displace the oxygen that you like using to live. Prop a window...
Space is that which separates particles. Time is that which allows particles to relocate in space.
I hear you describing discrete time or discrete space. As if they were pixels, refreshing on a computer screen. In those cases your question asks what happens when you 'beam' from one location to...
Question 2 Answer Below
When solving a double pendulum problem I built a Lagrangian of the form:
L(\theta_1, \theta_2, \dot{\theta_1}, \dot{\theta_2})
And found that my Euler Lagrangian equations for each coordinate where coupled to each other, as expected.
But I was a little confused about...
Question 1
When I take the derivatives of the Lagrangian, specifically of the form:
\frac{\partial L}{ \partial q}
I often find myself saying this:
\frac{\partial \dot{q}}{ \partial q}=0
But why is it true? And is it always true?
It would seem obvious how to proceed - solve for ω - but it is difficult to do directly.
Here's Wolfram Alpha's attempt at solving this:
A(ω) = \frac{F/m}{((ω_0^2 - ω^2)^2 + (γω)^2)^{0.5}}
Where ω0 = g0.5
We must keep out eyes for clever approximations.
Homework Statement
A simple pendulum has a length of 1m. In free vibration the amplitude of its swings falls off by a factor of e in 50 swings. The pendulum is set into forced vibration by moving its point of suspension horizontally in SHM with an amplitude of 1 mm.
a) [... Built Differential...