The only requirement is Python 3.8 or above
All used libraries are within the Python standard module
You don't need to install any extra module

👉 $m\cdot \ddot x = -\eta(t)\cdot \dot x -\kappa(t)\cdot x + \delta(t)$ ;

👉 where, $\delta(t)$ is Gaussian noise term

Take elasticity of the system: $\kappa (t),\ and$ viscosity of the system $\eta (t)$, defining the characteristic parameter of the system $\tau (t) \equiv \lambda (t) = \frac{\eta (t)}{\kappa (t)}$ 👉 Material-1: Exponential ageing $\rightarrow \lambda (t) = \exp (t/t_0)$

👉 Material-2: Power law ageing $\rightarrow \lambda (t) = (t/t_0)^m $

👉 The phenomena of 'ageing' is studied in microrheology via the Brownian motion of tracer bead particles. Hence, we appropriately modelled the materials and simulated the tracer bead trajectory for relevant insight.

👉 $\left< R^2 \right>\ \rightarrow\ mean\ sqaured\ displacement\ and,\ \ t, \xi \rightarrow\ simulation\ time$

👉 🌱 $My\ first\ humble\ contribution\ to\ Open-Source!!!$ 🌱