Which strategy should I use to approach a problem? Sometimes I'll use U = 1 / 2 k x 2 when I should use F = − k x and vice versa. What are clues in a problem that would let me identify the correct approach to a given problem? And shouldn't both approaches give me the same answer in any scenario?

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Which strategy should I use to approach a problem? Sometimes I&#039;ll use   U  =  1      /    2  k      x    2   when I should use   F  =  −  k  x and vice versa. What are clues in a problem that would let me identify the correct approach to a given problem? And shouldn&#039;t both approaches give me the same answer in any scenario?

Mario Dorsey · Accepted Answer

Obviously both are equivalent, in terms of applicability (you get the second directly by taking the gradient of the first).My &quot;rule of thumb&quot; is that for simple exercices,the energy view is more suited for initial/final state problems (like, &quot;find the end velocity of mass&quot; or &quot;find the maximal stretch of the spring&quot;) because you don&#039;t have to integrate the force,the force view is more suited for trajectory problems (like &quot;find the position of the mass as a function of time&quot;) because you don&#039;t have to derivate the energy.Of course that&#039;s only a way to choose one way to start solving a given problem; most of the time both are perfectly usable.When going to more complicated problems however this &quot;rule&quot; is not necessary true ; in any case you should choose the one that gives you as little unnecessary information as possible - while still answering the question.

ye1neh4 · Accepted Answer

Force is just minus gradient of U. Gradient is just (spatial) derivative.  F  =  −      d          d      x                  k              x        2              2    =  −            2      x      k        2    =  −  k  xSo, if your task has &quot;differential&quot; nature, it will probably suitable for force method. And if your task has &quot;integral&quot; nature, then it will probably suitable for potential method.

Which strategy should I use? Sometimes I'll use U=1/2kx^2 when I should use F=−kx and vice versa.

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