Review problem for classical, help please (1 Viewer)

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Review problem for classical, help please!!!

Hi I just started my classical mechanics class, and I was given this: a bunch of problems (image attached) (and one that I pulled from the notes I didnt know how to do as well.) that I could do for practice to refresh for the class, problem is I have no clue where and how to do any of these problems! I'm lost and this is the reivew :-( could anyone please help me figure out how to do these, I need to make sure i know how these are done for my quiz which i'm told is similar to these types of probelms or at least if I know how to do these I will be fine this friday.

A) Given ((mdx^2)/(dt^2))=F(x)
prove conservation of energy


To prove conservation of energy, I assume that you want to derive the work-energy theorem. Start with Newton's 2nd law and remember that you can express the time rate of change of velocity (dv/dt) in terms of its space rate of change(dv/dx) as follows:

(dv/dt) = v (dv/dx)

Hint: you will need to use the product rule of differentiation, but in a indirect way...
Can any one help me with the review problems in my image please?
Can any one help me with the review problems in my image please?
integrate xdoubledot=0. to find xdot and x. If you have problems with xdoubledot review...if you can't ...then perhaps analyical mech is not for you.

when you find hte general solution by integration solve for each selected problem given the parameters into xdot and x

question2. force of g-force - force of friction. Review your undegrad text for terminal velocity.

question3. there's a physics link to again review your text(phys or calc). Find how to find a period given a trig function then find itfor the summation of a trig function. Differentiate the given equation for b.

For c i hope you remember how to solve a linear system because thats what there asking...subs given values of x,t get 2 equations and solve.

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