This video just makes the entire thing more confusing lol

When you go to the next blank page, always keep the equation from last one visible. Love these videos btw!

@sameerdumne6965

2 ай бұрын

I second that

I'll have to do this one. I don't remember how I use to do this from scratch, but it'll be a great refresher. :)

I was so confused with this before. thank you

Thank you I finally understand this! I didn’t anticipate that it would involve a little Taylor series action!

when you said θ(t) = Acosωt + Bsinωt, why did you decide to put omega inside the sine and cosine?

@rohith5062

Ай бұрын

look up on how to solve a second order linear differential equation

General Relativity has a lot of explaining to do! :)

Physics was easy but greek letters ruined it

@omnigod7624

2 ай бұрын

True

Thank you for this video. At 3:25, isn't the acceleration always directed towards the centre in circular motion? Surely therefore there is no component in the direction of s to plug into F=ma?

@DotPhysics

10 ай бұрын

The tension does indeed pull in the center direction, but not the gravitational force. This means the net force is not in the r-hat direction.

@kaeez

14 күн бұрын

What you're referring to here is the centripetal force which facilitates circular motion. The centripetal force here is provided by the tension in the string. The gravitational acceleration is provided by the gravitational force.

Could I ask why you have to let theta is small before the next step?

@DotPhysics

Жыл бұрын

If theta is small, then you can let sin(theta) = theta. That makes the differential equation solvable by guessing a solution. It will look just like a simple harmonic oscillator.

I found a different way to derive, but im not sure if its correct. force of gravity = centripetal force? mg = mw^2 L w^2 = g/L w = (g/L)^1/2 is it a correct way to derive?

@DotPhysics

Жыл бұрын

But the gravitational force is down and the acceleration is up. This doesn't work.

@trickyepithet9122

Жыл бұрын

@@DotPhysics ahh alr

hey professor, could you teach us how to solve extreme distance free fall problems?

@DotPhysics

2 жыл бұрын

What is an example of an "extreme distance free fall" problem?

@HigorMadeira97

2 жыл бұрын

like when should consider the gradient of gravity, like a tennis ball falling the same distance from the moon to earh, since the gravity will change in some rate, and obviously the acceleration will not be as the same as earth surface. i think would be very nice see how it is done.

@shivanach45

8 ай бұрын

​@@HigorMadeira97 You'd need to use differential equations and g (now a variable) would be GM / R where G is the universal gravitation constant, M is the mass of the earth and R is the distance between the point mass (assume tennis ball to be a point mass) and Earth's centre . Essentially, we are having g to vary with distance here.

I don't see how x(t) = Acos(wt).

Why can we say w=2*pi*f?

@kathode1

5 ай бұрын

angular frequency (ω) is defined as the amount of radians an oscillator undergoes per second, which would be 2πf because frequency is the amount of cycles and there are 2π radians/cycle

Why the θ(t) = Acosωt + Bsinωt ?

@DotPhysics

Жыл бұрын

not theta(t), but f(t) - right? It's a function that satisfies the differential equation. If you take the derivative twice, you get the same function with a negative constant out front.

❤good

If you really want to understand this.. you need to know how to solve linear differential equations with constant coefficients and complex numbers. Requires more than just physics.

messy presentation

@skyrofia4670

3 ай бұрын

it was nice