yes, i get it but if dx/dt = 0, which it can, then the equation is satisfied and the other term doesn't have to be zero. However, we are saying the other term must always be zero.
U = energy
In the book:
\frac{dU}{dt} = \frac{d}{dt} (\frac{1}{2} mv^2 + \frac{1}{2} kx^2)
then we have m \frac{d^{2}x}{dt^2} + kx = 0 because v = \frac{dx}{dt}
however they get rid of \frac{dx}{dt} .
They are ignoring the case where v = 0, because then m \frac{d^{2}x}{dt^2} + kx...
If {x} is a sequence of rationals, I understand every real number will be a limit point. However, sequences have an order to them, right? So if this sequence of all rationals is monotonically increasing, then it will converge to infinite and all subsequences will have to converge to infinite. If...
I found this on a previous thread and someone mentions that you can use calculus to solve it. I already solved it using the law of conservation and got .027816 m or 2.7 cm, but it's driving me nuts figuring out how to use calculus to solve.
How do I go about integrating acceleration since...
1. A block of mass 0.3 kg and spring constant 24 N/m is on a frictionless surface. If the block is set into motion when compressed 3.5 cm, what is the maximum velocity of the block? How much is the spring compressed when the block has a velocity of 0.19 m/s?
Homework Equations
I found this...
The values and goals that Gore's dad had for Al Gore, continue to be remembered and followed by Gore. It was his dad,a Senatior, who helped instill in him the dream of becoming a president, and thus he ran in 2000. Gore's method of speaking and debating and even his political ideologies are...