Questions: Step 3 Find ω using the formula to find the period of the curve. period = (2 π) / ω Substitute the value of period and solve for ω, simplifying fractions. Your answer cannot be understood or graded. More Information = (2 π) / ω ⇒ ω = π / square Therefore, the model for simple harmonic motion is d = square

$Step 3 Find ω using the formula to find the period of the curve. period = (2 π) / ω Substitute the value of period and solve for ω, simplifying fractions. Your answer cannot be understood or graded. More Information = (2 π) / ω ⇒ ω = π / square Therefore, the model for simple harmonic motion is d = square$

Transcript text: Step 3 Find $\omega$ using the formula to find the period of the curve. \[ \text { period }=\frac{2 \pi}{\omega} \] Substitute the value of period and solve for $\omega$, simplifying fractions. $\square$ Your answer cannot be understood or graded. More Information $=\frac{2 \pi}{\omega}$ \[ \Rightarrow \omega=\frac{\pi}{\square} \] Therefore, the model for simple harmonic motion is $d=$ $\square$

Solution

Solution Steps

To find $\omega$, we need to use the given formula for the period of the curve. We will substitute the given period into the formula and solve for $\omega$. This involves rearranging the formula and simplifying the fractions.

Solution Approach

Start with the formula for the period: $\text{period} = \frac{2\pi}{\omega}$.
Substitute the given period value into the formula.
Rearrange the formula to solve for $\omega$.
Simplify the resulting expression to find $\omega$.

Step 1: Given Period

We are given the period of the curve as $ \text{period} = 4 $.

Step 2: Use the Period Formula

The formula for the period in terms of $ \omega $ is given by: \[ \text{period} = \frac{2\pi}{\omega} \] Substituting the given period into the formula, we have: \[ 4 = \frac{2\pi}{\omega} \]

Step 3: Solve for $ \omega $

Rearranging the equation to solve for $ \omega $: \[ \omega = \frac{2\pi}{4} = \frac{\pi}{2} \]