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Energy and Circular Motion

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  Energy in SHM & Circular Motion  When an object oscillates, its energy is constantly changing forms. Even though the motion looks simple, there’s a beautiful energy exchange happening underneath. And surprisingly, SHM is deeply connected to uniform circular motion: a connection that helps explain why SHM looks so smooth and predictable. Let’s break it down clearly. Energy in SHM In Simple Harmonic Motion, energy moves back and forth between potential energy and kinetic energy . 1. Potential Energy (PE) This is the energy stored when the object is stretched or compressed. For a spring: P E = 1 2 k x 2 PE is largest at the edges PE is zero at the center 2. Kinetic Energy (KE) This is the energy of motion. K E = 1 2 m v 2 KE is largest at the center KE is zero at the edges 3. Total Mechanical Energy Even though PE and KE change, the total energy stays constant (as long as there’s no friction or damping). This constant energy is what keeps the motion repeating smoothly. H...
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Velocity, Acceleration, and Net Force

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  Velocity, Acceleration, and Net Force When an object oscillates, it doesn’t move at a constant speed. Instead, its velocity , acceleration , and net force are always changing as the object moves back and forth. Understanding how these three quantities behave is the key to understanding Simple Harmonic Motion (SHM). Let’s break it down in a clear, student‑friendly way. Velocity in SHM Velocity tells us how fast the object is moving and in which direction. In SHM: At the center , the object moves the fastest At the edges , the velocity becomes zero The object speeds up as it moves toward the center It slows down as it moves away from the center This happens because the restoring force is always pulling the object back toward equilibrium. Acceleration in SHM Acceleration tells us how quickly the velocity is changing. In SHM: Acceleration is largest at the edges Acceleration is zero at the center It always points toward equilibrium So when the object is far from the center, the rest...
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Oscillation

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Linear Restoring Forces

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Linear Restoring Forces Have you felt a spring return back to its original length after stretching it? Or seen a pendulum swing and come back to the center? Both of these systems have a restoring force that pulls the object back toward equilibrium. And when that restoring force is linear meaning it increases evenly as you move farther away, the motion becomes Simple Harmonic Motion (SHM) . Hooke’s Law The equation for the restoring force of a spring is described by Hooke’s Law: F = − k x x is how far the mass is stretched or compressed k is the spring constant (how stiff it is) The negative sign means the force always points back toward equilibrium A bigger stretch means a bigger force towards equilibrium. This is what makes the motion smooth and predictable. Why Linear Forces Create Sinusoidal Motion When the restoring force is proportional to displacement, Newton’s Second Law becomes: m a = − k x or a = − k m x This tells us: Acceleration is highest at the highest displacement fr...
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