Menu

Energy in SHM

Part of the Mechanics section of Coddy's Physics journey. Lesson 85 of 97.

The total energy stays constant, shared between the spring and the block:

$\tfrac{1}{2}kx^2 + \tfrac{1}{2}mv^2 = \tfrac{1}{2}kA^2$

Energy of an oscillator against its position x from minus A to A: the elastic energy is a U-shaped curve, zero at 0 and largest at the ends; the kinetic energy is an upside-down U, largest at 0 and zero at the ends; their sum is a flat line, the total energy

Elastic plus kinetic energy is the same at every position.

At $x = \pm A$ : all elastic, the block stops. At $\relax x = 0$ : all kinetic, the speed is largest.

Challenge

A $0.2\ \mathrm{kg}$ block oscillates on a spring with $k = 80\ \mathrm{N/m}$ and a total energy of $2.5\ \mathrm{J}$ . Find its speed $v$ as it passes $x = 0.15\ \mathrm{m}$ .

Try it yourself

Physics diagram: path, spring, crate; arrows v = ?

Solve for $v$

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Mechanics

1Introduction

What is Physics?Your First Equation Turning a Rule Around

4Inclined Planes

Forces on an Incline Gravity Components Frictionless Incline Incline with Friction Will It Slide?Recap - Ramp Challenge

7Projectile Motion

Independent Axes Horizontal Launch Launch at an Angle Range and Max Height Recap - Hit the Target

10Work and Energy

Work Kinetic Energy Work-Energy Theorem Gravitational PE Conservation of Energy Power Recap - Roller Coaster

13Impulse and Momentum

Momentum Impulse Conservation of Momentum Elastic Collisions Inelastic Collisions Recap - Air Track

16Simple Harmonic Motion

What is SHM?Mass on a Spring The Pendulum SHM GraphsEnergy in SHMRecap - Oscillator

3Friction

What is Friction?Static Friction Kinetic Friction Friction and Newton's Laws Recap - Sliding Crate

6Vertical Motion

Free Fall Throwing Upward Time in the Air Recap - Dropped Ball

9Project: Delivery Drone

Mission Briefing Takeoff Thrust Climb to Altitude Cruise and Brake Package Drop

12Elastic Energy

Elastic Potential Energy Spring Launchers Energy with Springs Recap - Spring Launcher

15Circular Motion

Uniform Circular Motion Centripetal Acceleration Horizontal Circles Vertical Circles Loop the Loop Recap - Car on a Curve

18Final Challenges

Recap - Stunt Ramp Recap - Crash Test Recap - Space Probe