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

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Write linear functions: word problems

Full solution

Q.

\newline

\frac{1}{2}

\newline

Correct

\newline

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

. This is the formula for the angular frequency

\newline

\omega

of a mass

\newline

m

suspended from a spring of spring constant

\newline

k

. Solve this formula for

\newline

k

\newline

Answer

\newline

Keyboar

Multiply by $m$ : Now, we need to get rid of the division by $m$ . To do this, we multiply both sides of the equation by $m$ . $\newline$ $m \cdot (\omega)^2 = m \cdot \left(\frac{k}{m}\right)$ $\newline$ On the right side, the $m$ in the numerator and the denominator cancel out, leaving us with: $\newline$ $m \cdot (\omega)^2 = k$
Isolate k: We have now isolated k on one side of the equation. The final equation is: $\newline$ $k = m \cdot (\omega)^2$ $\newline$ This is the solved equation for $k$ in terms of $m$ and $\omega$ .

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