Understanding Simple Harmonic Motion

understanding-simple-harmonic-motion

As you delve deeper into our physics tuition topics, you’ll encounter the notion of Simple Harmonic Motion. Oscillations are a critical part of the theory of how sound impacts the physical world- so let’s look at this in a little more depth.

Wait…oscillations?

There are many examples of oscillation in the real world. They’re responsible for the music coming from a musical instrument, machines that have regular repeating movement, like how your clock ticks. Mechanical oscillations occur wherever there is a repeating movement, even when it’s an electrical repeating change of current and voltage.

The mechanical oscillation is the simplest to envision because we can see it in action- the way pendulum swings, or how the seat of a swing rises and falls, are both oscillations, moving through a set of fixed positions.

What terms are important when addressing oscillations?

There are a couple of terms you need to know if you’re going to talk about harmonic motion and oscillation. Displacement is the key term to describe distance with oscillation. The direction is indicated by negative and positive signs. Amplitude refers to the ‘height’ of the oscillations. The peak value is the maximum ‘height’ of the peak where the peak-to-peak value is the distance from the lowest to the highest peaks. The time period is the time taken through one complete cycle, no matter where it’s measured from in the cycle.

There are a few important things to note here.  

  • Displacement will always be the highest at the extremes of the oscillation, but the velocity at the midpoint.
  • The mass of the oscillating object is at equilibrium when it hits the oscillation midpoint.
  • Inertia is what carries it through the midpoint.
  • At maximum displacement, speed will be zero
  • If you plot displacement and velocity, they will have the same shape, but not line up in time. This is the phase angle.

Equilibrium

Equilibrium position will be the midpoint of the two extremes of displacement. It’s also where the object will rest if there are no external forces applied. Force will act in the direction of the equilibrium position [this is called the restoring force]. The larger the displacement, the larger the restoring force, making it proportional to the distance of the swing from equilibrium. The key thing to note with restoring forces is they do not restore equilibrium. Enough force is generated that it pushes past equilibrium to the other side.

Why do oscillations stop?

In the real world, however, damping is the force that will allow the oscillation to lose energy. The most common damping force is friction. Displaced air and pivots act against the ability for the oscillation to become a perpetual motion. To keep the oscillation constant, you would have to apply external forces

Understanding simple harmonic motion is an interesting part of our JC physics tuition syllabus, and a pretty simple one to master well.