DEV Community: Aayush Shah

I Accidentally Nudged My Stylus on My Desk and Ended Up Writing a Kinematics Simulator

Aayush Shah — Mon, 19 Oct 2026 19:21:38 +0000

As a high school student in India preparing for competitive STEM exams (JEE Advanced), you spend 12+ hours a day knee-deep in Newtonian mechanics, coordinate transformations, and differential equations.

When you solve kinematics problems for months on end, your brain starts projecting vectors, friction coefficients, and normal forces onto practically everything in your peripheral vision.

One evening, in the middle of a marathon problem-solving session, I placed my digital drawing stylus horizontally on my tablet surface.

I stretched, bumped my desk, and the pen began to roll back and forth on its slightly asymmetrical barrel. It rocked to and fro, steadily losing momentum until it settled to a dead stop.

I glanced up at my monitor and froze.

My cursor had been tracking this movement across the screen. Because the stylus was rocking with physical friction, the displacement on the monitor wasn't random mouse jitter—it was a textbook, real-world demonstration of Damped Simple Harmonic Motion (SHM) unfolding in front of me.

Instead of getting back to my problem set, I opened VS Code.

The Underlying Physics: Modeling the Desk

In classical mechanics, damped harmonic motion is described by a second-order linear differential equation:

m \frac{d ^{2} x}{d t ^{2}} + b \frac{d x}{d t} + k x = 0

When mechanical damping is small (the underdamped regime), the exact position as a function of time describes an oscillation confined inside an exponentially decaying envelope:

x (t) = A e^{- γ t} cos (ω t + ϕ)

Where:

$A$ is the initial displacement amplitude in pixels.
$γ$ is the damping factor (the friction between the pen and the desk).
$ω$ is the angular frequency determined by the stylus barrel curvature.
$ϕ$ is the initial phase angle offset.

I wanted to build a web tool— Pendula — that could take raw human cursor movement, fit it to this exact differential equation, and calculate the physical friction coefficient of whatever object was rolling on your desk.

Engineering the Live Tracker: Turning Jitter into Curves

Browser mouse events provide raw pixel integers via $(e . c l i e n tX, e . c l i e n t Y)$ . Transforming noisy human motion into a clean theoretical model in real time required three steps:

1. 1D Dimensionality Reduction (PCA)

A rolling stylus moves along a single axis, but human hands rarely orient it perfectly horizontal or vertical. Using Principal Component Analysis (PCA) on a rolling buffer of mouse samples, the engine automatically extracts the primary axis of motion and projects 2D coordinates onto a normalized 1D displacement axis $x (t)$ .

2. Peak & Period Extraction

The engine registers local displacement peaks $x_{max}$ across time to calculate the empirical oscillation period:

T = \frac{2 π}{ω}

3. Curve Fitting via Simulated Annealing

Because human input has hand jitter and surface imperfections, fitting the data using standard gradient descent gets trapped in local minima.

Instead, Pendula runs an optimization loop using simulated annealing: it iteratively perturbs the theoretical parameters $(A, γ, ω, ϕ)$ to minimize the Mean Squared Error:

MSE = \frac{1}{N} i = 1 \sum N (x_{observed} (t_{i}) - x_{theoretical} (t_{i}))^{2}

Once settled, a live overlay displays the race: your raw blue cursor trail plotted side-by-side against the ideal orange mathematical curve.

🕵️ The Twist: Cheating My Own Math with JEE Physics

Once the first version was running with 95%+ accuracy on real pens, a devious thought struck me.

In JEE physics, one of the foundational geometric proofs you learn is that Simple Harmonic Motion is simply the 1D shadow of Uniform Circular Motion.

Knowing that Pendula projects 2D motion onto a 1D PCA axis, I realized I didn't actually need a rolling pen to get a 99% score. I could mathematically exploit my own optimizer with mouse gestures.

Here are the three exploits I used to break my own app:

1. The Inward Spiral (90%+ Fit Score)

If you draw a continuous spiral inward with your mouse, you are tracing a decaying polar curve:

r (t) = A e^{- γ t}

When the PCA projects this 2D spiral onto its 1D primary axis, the coordinate becomes:

x (t) = r (t) cos (ω t) = A e^{- γ t} cos (ω t)

This is literally the exact equation for Damped SHM! The 1D projection of a shrinking circle perfectly mimics a physical pendulum, and the optimizer awarded it a near-perfect score.

2. The Figure-8 Lissajous Curve (88%+ Score)

Drawing a decaying figure-8 creates a periodic, Lissajous-like oscillation. The 1D projection is noisy but repetitive enough to trap the Simulated Annealing engine in a high-scoring local minimum.

3. The Single Straight Swipe (99% Score)

The most blatant loophole: if you swipe your mouse in a straight line and brake to a stop, the optimizer sets frequency $ω \to 0$ . The equation collapses into pure exponential decay:

x (t) = A e^{- γ t}

The math engine saw zero oscillation and confidently declared the straight line to be a 99% perfect physical dampening!

🛡️ The Anti-Cheat Fix: Geometric Tripwires

To keep the simulator honest, I built a two-part validation tripwire into the post-analysis engine:

Orthogonal Variance Guard: The engine now continuously measures displacement along the minor (perpendicular) PCA axis. If your perpendicular spread exceeds 15% of the primary axis, Pendula catches you drawing 2D shapes (spirals or figure-8s) and rejects the run.
Path-to-Displacement Ratio: A real pendulum swings over the exact same territory multiple times—meaning total cumulative path length must be several times larger than the net spatial spread $(L_{path} ≫ Δ x_{max})$ . If the total distance traveled roughly equals the displacement, Pendula flags the run as a single straight swipe.

Play With It Live

You can test both the physics engine and the cheat detection right in your browser—no downloads or setup needed:

🎮 Live Interactive App: shahaayush265.github.io/pendula
💻 Open Source Repository: github.com/shahaayush265/pendula

(Tip: Open the pre-loaded .motion files in the app's Cheats menu to watch the anti-cheat system catch these mathematical loopholes in real time.)

Building software from first principles reminds me why I fell in love with both programming and physics: formulas on paper are great, but there's nothing quite like watching raw physical reality and code meet on screen.

Let me know your thoughts, and if you manage to find another mathematical loophole to break the engine, I’d love to hear it in the comments!

Why I Rebuilt VLC's Frontend in Rust & Tauri v2 as a High Schooler

Aayush Shah — Mon, 19 Oct 2026 19:01:59 +0000

I have used VLC Media Player for as long as I can remember. It is arguably the most reliable piece of software on the planet, throw a corrupted 2004 .avi file at it, and it will play it without flinching.

Yet, every time I open it on a modern display, the UI feels like a relic from the Windows XP era.

Electron-based alternatives look gorgeous, but they consume 600MB of RAM just to open an empty window. I wanted the best of both worlds: native speed, zero bloat, and a modern aesthetic.

So I spent the last few months rebuilding the media player experience from scratch.

The Architecture: Tauri v2 + Rust + React 19

The core constraint was memory and responsiveness.

Instead of bundling Chromium (Electron), I chose Tauri v2:

Backend (Rust): Handles low-level file I/O, IPC pipelines, and OS-level window management. Tauri's memory footprint hovers around 30–45MB.
Frontend (React 19 + TypeScript): Renders a fluid, frosted-glass Canvas HUD with auto-hiding controls, visual chapter scrubbers, and instant keyboard shortcuts.
Audio Processing: A dedicated 10-band graphic equalizer with pre-amplification.

What I Learned About Frame-Accurate Scrubbing

The hardest part was building a seekbar that didn't feel stuttery. Most web-based players trigger a re-render on every timeupdate event (approx. 4 times per second), causing the scrub head to snap awkwardly.

By separating the rendering timeline from the underlying media buffer with an interpolated RAF (RequestAnimationFrame) loop, scrubbing feels buttery smooth even with high-bitrate 4K files.

Try It Out

The project is open source under the MIT license, and I've published pre-built binaries for Linux:

GitHub Repository: shahaayush265/vlcreborn
Live Binary Releases: v1.0.0 Release

If you build desktop apps or love media playback systems, I'd love your thoughts and pull requests!

Best way to dual boot with Windows

Aayush Shah — Tue, 04 Oct 2022 08:42:58 +0000

Many people like linux and want to get it. But the problem is they don't even want tot erase Windows. The answer to this problem is Dual-Booting. In this tutorial, I'll show you the steps to dual-boot Zorin OS alongside Windows. Don't worry, it is totally Safe.

Installation

I am assuming you have Windows preinstalled. You need 50 gb free space on your main Hard Drive (C:).
1) First, Download the Zorin OS 16 ISO.
While it is downloading, we will split our drive.
2) Type 'disk management' in the start menu and open it. It should look something like this :-

2a) Now, on the bottom screen, right-click C: drive and click shrink.

2b) Type any value greater that 50,000 MB and click Shrink.

If 50,000 mb or 50 gb is not available then free up space. If in file explorer it shows free space more that what it shows in Disk Management, search command prompt in start menu, right-click, click on run as administrator, and paste the following command:-

powercfg.exe /hibernate off

2c) Right-click unallocated space and create new simple volume and just continue with default settings.

Now wait for the ISO to be downloaded.

3) Download and install Rufus

4) Plug in any USB drive and make sure it is empty because it will be formatted.

5) Open Rufus and Select your USB drive and your ISO file and click start. If it gives any warnings, just press ok.

6) Open the website of your device manufacturer and find your bootloader key. It can be downe by typing "your_device_company boot key" into google.

Now the next few instructions are to be seen on an external device because you'll need to restart this device.

7) Restart your device. When the screen goes black, press and hold until you see the boot screen :-

8) Choose your USB drive.

9) Choose the first option and press enter. When the install screen appears, choose "Install Zorin OS".

10) Select Language and continue.

11) Keep default keyboard layout and continue.

12) It is not neccessary to connect to internet. So you can continue.

13a) Important! Choose Something Else

13b) Now from the loaded list, correctly choose your own empty drive and click change.

13c) Change size to 1024. In the use as dropdown, choose Ext4 Journalling System. Tick Format the Partition. In mount point, select '/boot'. Click ok.

13d) Now select the remaining free space, change and Ext4 Journalling System. Make sure the size is set to full. Tick format. In mount point, select '/' click on, click continue and click install now!

14) Choose your location and continue.

15) Fill in your details. Computer name can be anything. Click continue. Installation is started successfully!

16) After it ends, click restart now and when it asks to remove usb do it and press enter.

17) Select Zorin and press enter. You're in Zorin.

18) Continue with installation.

If you get any error during installation, just put it in the comments.

Linux Distros To Choose From

Aayush Shah — Tue, 04 Oct 2022 07:55:42 +0000

There are a lot of linux distros to choose from. At first, it might be very confusing to choose one, but trust me you'll get what you need here!

Arch Linux

If you want a lightweight and smooth running distro, choose Arch. By default, there is no GUI in Arch. If you are experienced with linux servers, you can give it a shot!


Manjaro

You still want the lightweightness but not the hassle of running commands in terminal? You can get any Arch-based distro such as Manjaro.

Debian

The one made for programmers! Has the power of apt. Far more packages that Arch. But here's the catch! No GUI again. However, you still get the basic tools right built-in. And the cherry on the cake is, it is the most stable linux distro! It also has the best hardware support.


Zorin OS 16

A GUI approach would be Zorin, the OS that I use. Looks perfectly great! But beware! It is not completely open-source. You may also try Ubuntu, completely open-source.

Fedora

For the sys-admins out there. A great OS. But, it is more like Arch. Completely DIY. Neither as stable as Debian nor as unstable as Arch. A middle option. Here's a link to comparision between Debian and Fedore. Fedora vs Debian

Final Thoughts

I feel Debian works best for me. I use Zorin which is based on Ubuntu which is based on Debian. Very Complicated! But it works great. I switched to linux from Windows about a month ago and I was surprised by the looks of linux. Completely Unexpected! I feel it is actually better than Windows. But there are few reasons why Windows still exists on my computer. The biggest reason is MS Office. LibreOffice and OnlyOffice are nowhere close to MS Office.