How to Solve an Oscillation Problem in Physics Easily

"How to solve an oscillation problem in Physics easily?" I think many students have asked this question a lot. With me, there is a very general solution for all oscillation problem. I call it "the energy solution". "The energy solution" to solve an oscillation problem in Physics is a process contains three steps: first imagine that the system move a very small distance, second using "the law of conservation and conversion of energy" to establish an equation for the oscillation system, and then third using the differential calculus. This solution is very strong for mechanical oscillation, especially in a mechanical-electromagnetic system, you just can use this solution to solve the problem.

At first, I imagines that the system move a very small distance. I will make an example with the spring pendulum, a simple spring-supported mass. I imagine that the mass move a very small distance. I will call that small distance is "x". The distance, x, is very small that it's very close to zero. This point is very important for the differential calculus that I will use later.

Then, at second, I will use "the law of conservation and conversion of energy" to establish an equation for the oscillation system. "The law of conservation and conversion of energy" states that the total energy remains constant in an isolated system whatever the process occurring in the system. So I will establish the energy of the system at the period before and after the movement. Then, just establish an equation of the energy of two periods. But the important thing is I notice that there must be "x"-the small distance- in the equation. And I remember that in the energy of each period, I figure out all kind of energy that the system contains, including mechanical energy, internal energy, electromagnetic energy, and chemical energy.

And at third, I will use the differential calculus. But I do not use it like I do in pure mathematics. When I use differential calculus in Physics, I use it in Physics way. I remember all differential definition of all physics term. So I can use it when I need it. For example, I always remember instantaneous velocity is the derivative of distance as a function of time, instantaneous acceleration is the derivative of velocity as a function of time. Those are the most important physics differential definitions for mechanical oscillation problem. And because "x" is very small that it is very close to zero. So I can simple something that is related to "x". For example, "a" is an angle that is opposite with "x". So cos a=1 ( cos a is very close to 1). It will make your problem simpler.

So that is my three-step energy solution to solve oscillation problem in Physics: first imagine that the system move a very small distance, second using "the law of conservation and conversion of energy" to establish an equation for the oscillation system, and then third using the differential calculus. I have used that many times and I always successful!