Skip to main content

Read This, Then Take a Swing at Solving Simple Harmonic Motion Practice Problems

pendulum simple harmonic motion
Credit: Public Domain

By Andrew Bennett

What Is Periodic Motion?

Simple harmonic motion is a special type of repeating motion motion motion motion (sorry, I couldn't resist). Motion that repeats after a certain amount of time is called periodic motion, where the "period" means the amount of time it takes for the motion to repeat.

Simple Harmonic Motion: A Type of Periodic Motion

Simple harmonic motion is periodic motion that is caused by a restoring force that is proportional to the object's distance from its equilibrium position. Let's unpack that!

SHM Examples

The most common examples of objects that undergo simple harmonic motion are a pendulum and a mass vibrating on the end of a spring. It turns out that atoms bonded to other atoms also undergo this type of motion. So, studying a pendulum helps us understand atomic motion and interactions.

We know that equilibrium is the state in which all the forces and torques on an object are balanced, so that the object is not accelerating. When a pendulum is resting in its vertical position, it is in equilibrium. If a mass is hanging down from a spring, there is one spot where the spring force exactly balances out the gravitational force. For a mass attached to a horizontal spring, there is one position of the mass for which the spring is not stretched or compressed and, therefore, applies no force to the mass. In each case, there is only one location of the object at which it will be in equilibrium, so we call this spot the equilibrium position.

What Is the Restoring Force? 

If you shift a pendulum in any direction from its equilibrium position and release it, the pendulum "bob" (the weight at the end of the string) will accelerate back toward the vertical position. This is true of the mass on the spring, as well. There will always be a net force acting on the object that points it back toward the equilibrium position. This force (or combination of forces) will tend to "restore" the object to its equilibrium position, so we call it the restoring force.

Finally, motion that we classify as simple harmonic motion requires that the restoring force be proportional to the object's distance from the equilibrium position. For example, if I pull on the mass part of a mass spring system, causing the mass to shift 5 centimeters to the right, there will be a force from the spring pushing or pulling it back to the left. If I shifted it 10 centimeters instead, the force to the left would be twice as large.

Applying Calculations to Simple Harmonic Motion

Once we have established than an object is, in fact, undergoing simple harmonic motion, we can apply a variety of calculations to it. This includes methods of calculating the period (time for one cycle) or frequency (how many cycles are completed per unit of time). 

SHM Physics Video

In this video, you will learn:

  • The definition of simple harmonic motion.
  • Equations that can be applied to simple harmonic oscillators (objects that undergo simple harmonic motion).
  • How to use those equations in practice problems.


If viewing via email, click here to watch the video.

If you would like to try some more sample problems, check out these pages:

The Next Step Is Simple

For more information on simple harmonic motion, check out my AP Physics 1 - Simple Harmonic Motion playlist. While you're on YouTube, please subscribe to my channel. And to make sure you don't miss a post, please subscribe to this blog, as well. Thank you!

Comments

Popular posts from this blog

3 Easy Science Experiments to Do with Your Kids

By Amber Bennett Strong STEM (science, technology, engineering, and math) skills set kids up to succeed both in school and later in life. Encouraging them to be interested in these subjects is easier than you might think, especially if you start when they're young.  Activities that encourage children to be curious and creative will spark a love of learning. Plus, science experiments and other hands-on STEM projects are a fun way to bond with your kids. Here are three easy science experiments that preschoolers and early elementary students will enjoy. 1. Leakproof Plastic Bag A (age 5) doing the leakproof plastic bag experiment. Our preschooler loves to do any experiment that involves water. I can give her a couple of beakers, and she'll happily pour water back and forth between them, especially if I put a few drops of food coloring in each beaker so she can mix the colors.  Another great activity that involves water is the leakproof plastic bag.  All you need are: Large plastic

Why Do They Do That? The Physics Behind 3 Famous Animal Behaviors

By Amber Bennett Have you ever wondered about the origins of the phrase, "get your ducks in a row"? What about how the "doggy paddle" works or why squirrels are such amazing jumpers? The answers to all of these questions have one thing in common: physics. Keep reading to learn about the science behind these three famous animal behaviors. How Do Squirrels Leap from Branch to Branch? A squirrel leaps through the air.  Photo Credit:  caroline legg ,  CC BY 2.0 , via  Wikimedia Commons The death-defying acrobatic maneuvers performed by squirrels look a lot like parkour tricks. But how do they know how to land tricky jumps between bendy tree branches that move with the wind?  Researchers say  it's a combination of learned behavior (practice makes perfect) and inherited adaptations.  To see what determines how far a squirrel is willing to jump and how the leaps are timed, researchers set up an obstacle course in an artificial forest. Then, they used peanuts to encoura

How Virtual Currency Mining Is Hurting the Environment - Science in the News

Datacenters used for cryptocurrency mining use a lot of energy. By Amber Bennett Although cryptocurrencies are virtual, they are having a tangible impact on our environment. Research shows that cryptocurrencies actually are worse for the earth than other types of money. So, why is that? Simply put, it's because of the resources needed to run the supercomputers that mine Bitcoin and other virtual currencies.  Energy Use The datacenters used for mining use large amounts of electricity. For example, the global Bitcoin network uses  more energy than entire countries . In fact, according to the University of Cambridge Bitcoin Electricity Consumption Index , the network's power demand is the same as more than 14 million typical American homes. Most of the energy used in the datacenters comes from fossil fuels instead of renewable resources. Plus, datacenters' high energy use can destabilize the electric grid. Materials Mining Another way that cryptocurrency impacts the environme