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In this section, we derive equations of motion for a number of simple systems, and find their solutions.The purpose of these examples is to illustrate the straightforward, step-by-step procedure for analyzing motion in a system.

The Direction of the air drag force is always opposite to the direction of motion of the projectile through the air.

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.

the deflection of the spring due to the weight of the vehicle (without motion).

This means that the car vibrates symmetrically about its static deflection. You are, of course, familiar with how a pendulum can be used to measure time.The constraints must be expressed in terms of the unknown accelerations.Identify the initial conditions for the variables defined in (1).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.