Question

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Answer 1

$\omega \ in \ terms \ of \ m \ and \ k \ is\ expressed \ as \ \omega = \sqrt{\frac{k}{m} }$

• The given expression is as follows;

     $T_s = 2\pi \sqrt{\frac{m}{k} } , \ \ \\\\ T_s = \frac{2\pi}{\omega}$

• To find ω in terms of m and k;

From the given expression above make ω the subject of the formula;

$T_s = \frac{2\pi}{\omega} = 2\pi \sqrt{\frac{m}{k} } \\\\ \frac{2\pi}{\omega} = 2\pi \sqrt{\frac{m}{k} }\\\\ \frac{2\pi}{\omega} = \sqrt{4\pi^2\frac{m}{k} }\\\\square \ both \ sides \ of \ the \ equation;\\\\(\frac{2\pi}{\omega})^2 = 4\pi^2\frac{m}{k} \\\\\frac{4\pi^2}{\omega^2}= \frac{4\pi^2m}{k} \\\\\omega^2 4\pi^2m = k4\pi^2 \\\\divide \ both \ side \ by \ 4\pi ^2 \\\\\omega^2 m = k\\\\divide \ both \ sides \ by \ m\\\\\omega^2 = \frac{k}{m}$

$take \ the \ square \ root \ of \ both \ sides \ of \ the \ equation\\\\\omega = \sqrt{\frac{k}{m} }$

Therefore, ω in terms of m and k is expressed as $\omega = \sqrt{\frac{k}{m} }$

To learn more about subject of formula visit: brainly.com/question/15469690