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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!
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