# Eom dating method

Estimate the maximum height above the surface that a typical particle can reach during its thermal motion, assuming that the only force acting on the particles is gravity Recall the spring force law, which says that the forces exerted by a spring act parallel to its length, tend to shorten the spring, and are proportional to the difference between the length of the spring and its un-stretched length. Here, mg/k is the static deflection of the spring i.e.the deflection of the spring due to the weight of the vehicle (without motion).But there is no way to check the assumption at this point so we simply proceed, and check the answer at the end In this problem, it is helpful to eliminate the unknown reaction force R.You can do this on the computer if you like, but in this case it is simpler to do this by hand. Solve the equations of motion This equation of motion is too difficult for Mathematica (it can come close to getting a solution if you don’t specify any initial conditions) but actually the solution does exist and is very well known The first solution describes swinging motion of the pendulum, while the second solution describes the motion that occurs if you push the pendulum so hard that it whirls around on the pivot.If you happen to know the values of the variables at some other instant in time, you can use that too.If you don’t know their values at all, you should just introduce new (unknown) variables to denote the initial conditions.The general process described in the preceding section can be illustrated using simple examples.

If calculations predict that the internal force is compressive, this assumption is wrong.

I have a [r] large data frame with date variables, which reflect first day of the month.

Is the a easy way to crete a new data frame date variable that represents the last day of the month?

More detailed discussions of the behavior of dynamical systems will follow in later chapters.8. In general we will use MAPLE or matlab to do the rather tedious algebra necessary to solve the equations of motion.

Here, however, we will integrate the equations by hand, just to show that there is no magic in MAPLE.: It is traditional in elementary physics and dynamics courses to solve vast numbers of problems involving particle trajectories.

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