#AP Physics 1: Simple Harmonic Motion - The Night Before 🌃

Hey! Let's get you totally prepped for Simple Harmonic Motion (SHM). This guide is designed to be super clear, quick to use, and exactly what you need for a great score tomorrow.

#1. What is Simple Harmonic Motion?

Simple Harmonic Motion (SHM) happens when an object is pulled back to its equilibrium point by a force that's proportional to how far it is from that point. Think of it like a spring or a pendulum swinging back and forth. 💡

• Key Examples:
  • Mass on a spring (obeying Hooke's Law)
  • Pendulum (small angle displacement)

#2. Newton's Second Law & SHM

#Applying Newton's Second Law

Newton's second law, F = ma, is your go-to for analyzing motion. Here's how to use it with SHM:

1. Identify Forces: Figure out all the forces acting on the object (gravity, spring force, etc.).
2. Free-Body Diagram: Draw a diagram showing all the forces.
3. Mass & Acceleration: Note the object's mass and its acceleration.
4. F = ma Equation: Write the equation for the sum of forces: F = ma.
5. Solve for Acceleration: Plug in known values and solve for 'a'.
6. Velocity & Position: Use acceleration to find velocity (v = at) and position (x = at²/2).
7. Graph It: Visualize the motion by graphing velocity and position vs. time.
8. Solve Unknowns: Use equations to find things like the spring constant or initial displacement.
9. Repeat: If there are multiple objects, repeat the process for each.

#3. Restoring Force: The Heart of SHM

#What's a Restoring Force?

A restoring force is like a guide that pulls an object back to its happy place—its equilibrium position. This force is what causes the back-and-forth motion in SHM.

• Key Points:
  • It always pulls the object back to equilibrium.
  • Common in oscillating systems (pendulums, springs).
  • It's opposite to the object's displacement from equilibrium.
  • Can be caused by gravity, elastic forces, friction.
  • The strength is measured by the spring constant (k).
  • The force is calculated as F = -kx (...