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Question 2 of 2, Step 1 of 1
Correct

omega=sqrt((k)/(m)). This is the formula for the angular frequency
omega of a mass
m suspended from a spring of spring constant
k. Solve this formula for
k.
Answer

Question $2$ of $2$ , Step $1$ of $1$ $\newline$ Correct $\newline$ $\omega=\sqrt{\frac{k}{m}}$ . This is the formula for the angular frequency $\omega$ of a mass $m$ suspended from a spring of spring constant $k$ . Solve this formula for $k$ . $\newline$ Answer

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Write and solve direct variation equations

Full solution

Q. Question

2

of

2

, Step

1

of

1

\newline

Correct

\newline

\omega=\sqrt{\frac{k}{m}}

. This is the formula for the angular frequency

\omega

of a mass

m

suspended from a spring of spring constant

k

. Solve this formula for

k

.

\newline

Answer

Start Formula Angular Frequency: Start with the given formula for angular frequency. $\newline$ $\omega = \sqrt{\frac{k}{m}}$ $\newline$ We need to solve for $k$ , which means we want to isolate $k$ on one side of the equation.
Square Both Sides: Square both sides of the equation to eliminate the square root. $\newline$ $(\omega)^2 = (\sqrt{k/m})^2$ $\newline$ This simplifies to: $\newline$ $\omega^2 = k/m$
Multiply by $m$ : Multiply both sides of the equation by $m$ to isolate $k$ .
$m \cdot \omega^2 = \left(\frac{k}{m}\right) \cdot m$
This simplifies to:
$m \cdot \omega^2 = k$
Isolate $k$ : We have now isolated $k$ on one side of the equation. $k = m \cdot \omega^2$ This is the formula for $k$ in terms of $m$ and $\omega$ .

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