A simple harmonic oscillator a time period of 10s, write an equation relates it's acceleration and displacement x

Step 1: The general equation for acceleration $a$ in simple harmonic motion (SHM) is given by: $a = -\omega^2 x$ where $\omega$ is the angular frequency and $x$ is the displacement.

Step 2: Calculate the angular frequency $\omega$ using the given time period $T = 10$ s. $\omega = \frac{2\pi}{T}$ $\omega = \frac{2\pi}{10 s}$ $\omega = \frac{\pi}{5} \text{ rad/s}$

Step 3: Substitute the value of $\omega$ into the acceleration equation. $a = -\left(\frac{\pi}{5}\right)^2 x$ $a = -\frac{\pi^2}{25} x$

The equation relating acceleration and displacement is: $\boxed{a = -\frac{\pi^2}{25} x}$ Send me the next one 📸