# Solving a Motion Problem Using a System of Equations - Example 2

Animation applied in user interfaces is the topic drawing high attention and provoking hot debates nowadays. Although there is a big army of those who find animation an unnecessary feature overloading user interface and making it more complicated, most users expect motion as an integral part of interaction experience. So, designers and developers work over more and more sophisticated methods to make animation pleasant-looking and problem-solving characteristic of modern apps and websites.

## Simple Harmonic Motion and Introduction to Problem Solving

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### Here are some examples for solving motion problems.

Physics is an area of science which deals with how matter and waves behave in the Universe. A branch of physics called mechanics, deals with forces, matter and motion. A further sub branch known as kinematics deals with motion, and ballistics is specifically concerned with the motion of projectiles launched into the air, water or space. Solving ballistic problems involves using Newton's equations of motion.

### Solving Problems Using Motion equations

As mentioned, there are cases where the choice of sign convention doesn’t matter, but rather than attempt to list all these cases it is better to just be on the safe side and use the sign convention given here for solving problems using the equations of motion. You will never go wrong.

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Equations of motion relate the forces acting on a system to the motion of the system. These equations are generally the most useful because they allow for the direct solution of a dynamics problem, as a function of time. Using these equations one can determine the "behaviour" of a system over time, which can give important information as a result. On the other hand, solving dynamics problems using energy or momentum methods is generally only done if one wishes to determine the final state of a system based on some initial state, without regard for what happens "in between".Motion problems are among the most common word problems you’ll encounter on the Quantitative section of the GMAT. These problem solving questions fall into one of three categories:Any problem that asks you to describe the motion of an object without worrying about the cause of that motion is a kinematics problem, no matter what was given or requested in the problem. In some cases, you can use either kinematics or energy to solve a problem. However, if you are asked about time or horizontal motion you most likely will need to use kinematics.Using the Lagrangian method one can find the equations of motion for a system in a straightforward fashion, without having to go through a Newtonian analysis, in which you have to consider the forces acting on the system and assign directions, etc. This can save some time and effort. However, the catch is that the Lagrangian method only works when there are acting on the system, and there is no friction anywhere. Furthermore, you can lose some "feel" for the problem since you are going directly to the mathematics rather than analyzing the physics first (which comes from considering the forces acting on the system). So it is perhaps not a good idea to use this method if you are still gaining proficiency solving classical mechanics problems. However, if you are already an experienced problem solver, the Lagrangian method is an efficient way to solve problems, saving you time and effort.