Yo-yoing over the harmonic oscillator

AI Thread Summary
The discussion centers on understanding how the cosine function appears in the solution to the harmonic oscillator equation, d²x/dt² = -kx/m. The user seeks clarification on the relationship between the second derivative of the cosine function and the equation's structure. It is noted that the second derivative of -cos(θ) equals cos(θ), which aligns with the harmonic oscillator's characteristics. Additionally, the suggestion to explore the form x = a*cos(bt) is presented as a potential solution fitting the equation. Overall, the conversation emphasizes the mathematical foundations of harmonic motion and the role of trigonometric functions in its solutions.
DiracPool
Messages
1,242
Reaction score
515
I've been looking around and trying to figure it out, but I can't seem to figure out how the cosine function get's into the solution to the HO equation d2x/dt2=-kx/m. I know this is extremely basic, but could someone indulge me?
 
Physics news on Phys.org
It is not so difficult to use a better notation!

Try to see whether x = acos(bt), where a and b are constants, fits with the equation

\frac{d^{2}x}{dt^{2}} = -(positive constant)x.
 
Thread 'Question about pressure of a liquid'

Thread 'Question about pressure of a liquid'

I am looking at pressure in liquids and I am testing my idea. The vertical tube is 100m, the contraption is filled with water. The vertical tube is very thin(maybe 1mm^2 cross section). The area of the base is ~100m^2. Will he top half be launched in the air if suddenly it cracked?- assuming its light enough. I want to test my idea that if I had a thin long ruber tube that I lifted up, then the pressure at "red lines" will be high and that the $force = pressure * area$ would be massive...
View full post »

Thread 'Why is the 3 body problem unsolvable? And what will happen if someone solves it?'

I feel it should be solvable we just need to find a perfect pattern, and there will be a general pattern since the forces acting are based on a single function, so..... you can't actually say it is unsolvable right? Cause imaging 3 bodies actually existed somwhere in this universe then nature isn't gonna wait till we predict it! And yea I have checked in many places that tiny changes cause large changes so it becomes chaos........ but still I just can't accept that it is impossible to solve...
View full post »

Similar threads

B Harmonic oscillator and simple pendulum time period
Replies
36
Views
3K
I Damped oscillator with changing mass
3
Replies
131
Views
7K
A Equipartition theorem and Coupled harmonic oscillator system
Replies
3
Views
2K
Continuity Equation for a Dimensionless Harmonic Oscillator
Replies
16
Views
2K
B Determining ansatz for forced oscillations in SHM
Replies
1
Views
1K
I How Does Changing Mass and Spring Force Affect Watch Oscillators?
Replies
11
Views
2K
Derive equation for Energy of the Harmonic Oscillator
Replies
13
Views
3K
Oscillation of free surface of water in parallelepiped container
Replies
13
Views
2K
A Pair of interacting systems, driven coupled harmonic oscillators
Replies
7
Views
2K
Quantum Harmonic Oscillator with Additional Potential
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top