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I shared a picture of the problem. It’s a basic Physics question and an Algebra question.

I Shared A Picture Of The Problem Its A Basic Physics Question And An Algebra Question class=

Sagot :

Hence the expression of ω in terms of m and k is

[tex]\omega = \sqrt{\frac{k}{m}[/tex]

Given the expressions;

[tex]T_s = 2 \pi \sqrt{\frac{m}{k} } \ and \ T_s = \frac{2 \pi}{\omega}[/tex]

Equating both expressions we will have;

[tex]2 \pi \sqrt{\frac{m}{k} } = \frac{2 \pi}{\omega}[/tex]

Divide both equations by 2π

[tex]\frac{2 \pi\sqrt{\frac{m}{2 \pi} } }{2 \pi}=\frac{\frac{2 \pi}{\omega} }{2\pi}\\\sqrt{\frac{m}{2 \pi} } = \frac{1}{\omega}\\[/tex]

Square both sides

[tex](\sqrt{\frac{m}{k} } )^2 = (\frac{1}{\omega} )^2\\\frac{m}{k} = \frac{1}{\omega ^2} \\\omega ^2 = \frac{k}{m}[/tex]

Take the square root of both sides

[tex]\sqrt{\omega ^2} =\sqrt{\frac{k}{m} } \\\omega = \sqrt{\frac{k}{m}[/tex]

Hence the expression of ω in terms of m and k is

[tex]\omega = \sqrt{\frac{k}{m}[/tex]

Learn more about subject of the formula here: https://brainly.com/question/19557491

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