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

June 18, 2026Physics

ScanSolve AI Answer

June 18, 2026

Answer

$a = -\frac{\pi^2}{25} x$

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 📸

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Quick Answer

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

Asked on June 18, 2026Physics

This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.

ScanSolve AI AnswerAnswered on June 18, 2026

Step 1: The general equation for acceleration a in simple harmonic motion (SHM) is given by: a = -^2 x where is the angular frequency and x is the displacement. Step 2: Calculate the angular frequency using the given time period T = 10 s. = (2)/(T) = (2)/(10 s) = ()/(5) rad/s Step 3: Substitute the value of into the acceleration equation. a = -(()/(5))^2 x a = -(^2)/(25) x The equation relating acceleration and displacement is: a = -(^2)/(25) x Send me the next one 📸