Recent content by 693Janu

Imagine that, I was given initial velocity.

This was fun! Thanks so much! Fantastic finish to a great weekend.

I had that intuition before I even read your post (personal high five), and it worked out! I have two solutions and I can now solve for Initial conditions. That's great! However, the last tricky step is finding the period. How would I find the period with two different omega values? Because I...

Great advice, thank you so much. However, I have never done this discussed "change of coordinates before". I do see how after adding the two equations together I can say... let $$u=x+y$$ and that gives a nice SHM solution. But how do I extract x(t) from that answer? Or do I even need to?

I was given initial coordinates $$(3,4)$$

I am tasked with finding the path a particle takes through this potential field. $$U(x,y) = x^2+xy+y^2$$ I then took the gradient, and this produced a pair of differential equations. $$\frac{d^2x}{dt^2}=\frac{1}{m}(-2x-y)$$ $$\frac{d^2x}{dt^2}=\frac{1}{m}(-2y-x)$$ I have yet to encounter set of...

Take the time, I know you may feel like you "Need" to get things done quickly. This is true in some cases but I think you might find in this case it was the better choice to take your time, do the summer research, and extend out your stay for one year. Good luck!