Please provide a rating, it takes seconds and helps us to keep this resource free for all to use
In addition to the revision notes for Simple Harmonic Motion on this page, you can also access the following Oscillations learning resources for Simple Harmonic Motion
Tutorial ID | Title | Tutorial | Video Tutorial | Revision Notes | Revision Questions | |
---|---|---|---|---|---|---|
10.2 | Simple Harmonic Motion |
In these revision notes for Simple Harmonic Motion, we cover the following key points:
By definition, "Simple harmonic motion (in short SHM) is a repetitive movement back and forth through an equilibrium (or central) position, so that the maximum displacement on one side of this position is equal to the maximum displacement on the other side."
In other words, in simple harmonic motion the object moves back and forth along a line. These back and forth movements are known as "oscillations". Simple harmonic motion is part of a wider category of motion known as "periodic motion", which includes other types of motions that repeat themselves such as circular, vibrational and other similar motions. However, simple harmonic motion and periodic motion are not the same thing. There are two main differences between them.
Based on the trajectory (path) of the oscillating object, there are two types of simple harmonic motion.
The function that describes better mathematically a SHM, is the sine (or cosine) function. This is because of two main reasons:
In mathematics, the simplest sine function in which the time t is the independent variable and the position x is the dependent one, has the form
If the graph does not start at the origin but it is shifted from it, we insert the angular displacement φ in the above equation, so it becomes
The initial angular displacement φ here is known as the "phase shift".
From calculus it is known that the first derivative of position with respect to time (dx/dt) represents the velocity v and the second derivative of position with respect to time d2x/dt2 (or the first derivative of velocity in respect to time dv/dt) gives the acceleration a.
Applying the above derivation rules for the SHM motion, we obtain for the velocity v in respect to the time, v(t):
and for the acceleration a in respect to the time, a(t):
Therefore, we obtained a very important formula of SHM that relates acceleration a, angular frequency ω and displacement x:
Since the restoring force F is in the opposite direction to the acceleration a, we obtain from Newton's Second Law of Motion for the acting forces in springs:
where m is the mas of hanged object and k is the spring constant. Thus,
Hence,
Or
Then we can substitute this value of angular frequency in the sine equation of SHM if an object hanged on an elastic spring causes oscillations.
Enjoy the "Simple Harmonic Motion" revision notes? People who liked the "Simple Harmonic Motion" revision notes found the following resources useful:
Please provide a rating, it takes seconds and helps us to keep this resource free for all to use
We hope you found this Physics tutorial "Simple Harmonic Motion" useful. If you did it would be great if you could spare the time to rate this physics tutorial (simply click on the number of stars that match your assessment of this physics learning aide) and/or share on social media, this helps us identify popular tutorials and calculators and expand our free learning resources to support our users around the world have free access to expand their knowledge of physics and other disciplines.