Simple Harmonic Motion Project

  The Connection Between Simple Harmonic Motion and Uniform Circular Motion At first glance, simple harmonic motion (SHM) and uniform circular motion (UCM) seem completely different. In SHM, an object moves back and forth along a straight line. In uniform circular motion, an object moves in a circle at constant speed. One is linear. The other is rotational. However, the truth is that simple harmonic motion is actually the projection of uniform circular motion onto a diameter of a circle. In other words, if you look at circular motion from the right perspective, it becomes SHM. Visualizing the Connection The graph above shows displacement changing smoothly and periodically over time. The object begins at equilibrium, moves to a maximum positive displacement, returns through equilibrium, continues to a maximum negative displacement, and then repeats the cycle. This repeating sinusoidal pattern is the defining feature of simple harmonic motion. The highest and lowest points on the ...

Energy in Simple Harmonic Motion When you watch a mass attached to a spring bounce back and forth, it can almost seem like the motion continues on its own. The mass speeds up, slows down, stops, and reverses direction without anyone pushing it again. The reason this happens is energy. In Simple Harmonic Motion (SHM), energy is never destroyed in an ideal system. Instead, it continuously shifts back and forth between potential energy and kinetic energy in a perfectly predictable pattern. In ideal SHM, meaning no friction or air resistance, the total mechanical energy of the system remains constant. Energy does not disappear or get created; it simply changes form. At every point in the motion, the system has some combination of potential energy (stored energy) and kinetic energy (energy of motion), but the total amount always stays the same. The Big Idea: Energy Is Conserved In ideal SHM (no friction, no air resistance): The total mechanical energy of the system stays constant. Ener...

Velocity, Acceleration, and Net Force in SHM  When a spring oscillates back and forth, or a pendulum swings through its arc, the motion appears smooth and rhythmic. However, beneath that motion, three quantities are constantly changing: velocity, acceleration, and net force. Understanding how these three interact is essential to understanding Simple Harmonic Motion. In SHM, the defining rule is that the net force always points toward equilibrium and is proportional to displacement. Because acceleration depends directly on net force through Newton’s Second Law, acceleration also always points toward equilibrium. Velocity behaves differently. Velocity depends on the direction the object is moving, not just its position. This distinction is what makes SHM conceptually interesting. Concept Explanation As an object moves away from equilibrium, the restoring force increases in magnitude. This means acceleration increases as displacement increases. At maximum displacement, the force and ...

Linear Restoring Forces Imagine pulling a spring to the right and letting go, or pushing a playground swing away from its resting position. In both cases, the object doesn’t just move randomly; it feels a force that always tries to bring it back to equilibrium.  That special kind of force is called a linear restoring force , and it’s one of the core concepts of Simple Harmonic Motion (SHM). What Is a Restoring Force? A restoring force is a force that always points towards the equilibrium position and becomes stronger the farther you move away from the equilibrium position. In SHM, this restoring force is linear , meaning the restoring force increases in direct proportion to the displacement from equilibrium. Double the displacement results in double the restoring force, while half the displacement results in half the restoring force. This linear relationship is what keeps the motion smooth, repetitive, and predictable. Linear Restoring Force in a Mass–Spring System Consider a mass...

Rishi Eti AP Physics 1 Mrs. Allen 3 February 2026 Period, Frequency, & Amplitude  When something moves back and forth over and over, such as a playground swing, a bouncing car suspension, or a mass on a spring, it is performing Simple Harmonic Motion (SHM). Before learning complicated equations, we need to understand the three ideas that describe every oscillation: Amplitude – how big the motion is. Period – how long one cycle takes. Frequency – how many cycles happen during a certain time frame (we will be using cycles per second). These three quantities are the “vocabulary” of SHM, and everything else in this unit builds from them. What Is Amplitude? Amplitude (A) is the maximum distance from the equilibrium position or the middle point where the object would naturally rest. For a mass-spring system: amplitude is how far the mass is stretched or compressed from the center. For a pendulum: amplitude is the farthest distance or angle the bob reaches from the lowest point. It ...