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
