Everyday simple harmonic motion problems come down to one relationship between amplitude (a), frequency (f), time (t), sin and cos. This calculator turns those numbers into angular frequency, acceleration (a) and displacement (y), with the working shown so you can check the result rather than simply trust it.
What Is the Simple Harmonic Motion Calculator?
This simple harmonic motion calculator is for the kind of problem where you know the physical quantities but not the number you need. It turns amplitude (a), frequency (f), time (t), sin and cos into angular frequency, acceleration (a) and displacement (y).
Physics calculations go wrong in predictable ways, usually through mixing units or dropping a digit. Work through the result one step at a time and check that the figures are the size you would expect at each stage.
How the Simple Harmonic Motion Physics Works
The relationship is applied step by step, and each step is a standard piece of physics rather than a single opaque formula. That means you can check the intermediate values against what the theory predicts, which is usually faster than checking only the final answer.
Keep every value in the same unit system throughout the calculation. Mixing metres and feet part way through is the single most common reason a correct formula gives a wrong answer.
Units, Assumptions and the Limits of the Model
The calculation assumes ideal conditions: no air resistance, no heat loss, and dimensions that do not change while you work. Those assumptions are reasonable for most classroom and engineering estimates, and unreasonable for anything more precise.
Where a value is a rate, it has to be quoted for the same period as everything else. A per-hour figure cannot be combined with a per-day figure without converting one of them first.
A Worked Example
Working through an example, with amplitude (a) set to 10, frequency (f) set to 5, time (t) set to 2, the calculator returns angular frequency of 31.41593, and velocity (v) of 314.15927, and acceleration (a) of 0. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out angular frequency?
Enter amplitude (a), frequency (f), time (t), sin and cos. The calculator then works through the relationship and reports angular frequency, acceleration (a) and displacement (y).
What does the simple harmonic motion actually calculate?
It takes amplitude (a), frequency (f), time (t), sin and cos and converts them into angular frequency, acceleration (a) and displacement (y) using the standard relationship for this problem. Each step is applied in turn, so every output is traceable back to the numbers you typed in.
How should I enter amplitude (a)?
Use the value you actually have, in the unit shown next to the field. Enter every value in the same unit system. The calculator assumes the figures you supply are consistent, so it cannot correct a mistake that happens before the calculation starts.
Is the answer exact?
It is as exact as the formula and the inputs allow. The method itself is the standard one for this problem, so the only sources of error are the figures you enter and the precision you ask for.
Why does a small change in one value move the answer so much?
That happens when an output depends on a ratio, because dividing by a small number magnifies any change in it. Check the units first, then check whether the value you entered is in the range the relationship was designed for.