Science Common Sense

1657 - What is simple harmonic motion and how can its displacement and velocity be expressed.

Imagine you're on a swing, moving back and forth. Simple harmonic motion (SHM) is a type of motion where you move in a straight line, but your speed and direction change in a regular, repeated pattern.

In SHM, you can use math to describe how you move. Your displacement (how far you are from the middle point) and velocity (how fast you're moving) can be expressed like this:

• Displacement: It's like a sinusoid curve, which looks like a wave. Mathematically, it's x(t) = A sin(ωt), where:
• x(t) is your displacement at time t
• A is the maximum displacement (the farthest you go from the middle)
• ω (omega) is the angular frequency (how fast you swing)

• t is time

• Velocity: As you move, your velocity changes too. Mathematically, it's v(t) = Aω cos(ωt), where:

• v(t) is your velocity at time t
• A is the maximum displacement (the farthest you go from the middle)
• ω (omega) is the angular frequency (how fast you swing)
• t is time

These equations help us understand how objects move in SHM, like a swinging pendulum or a vibrating guitar string.