Answer:
6 rad/s
Explanation:
In a spring the angular frequency is calculated as follows:
[tex]\omega=\sqrt{\frac{k}{m} }[/tex]
where [tex]\omega[/tex] is the angular frequency, [tex]m[/tex] is the mass of the object in this case [tex]m=2kg[/tex], and [tex]k[/tex] is the constant of the spring.
To calculate the angular frequency, first we need to find the constant [tex]k[/tex] which is calculated as follows:
[tex]k=\frac{F}{x}[/tex]
Where [tex]F[/tex] is the force: [tex]F=18N[/tex], and [tex]x[/tex] is the distance from the equilibrium position: [tex]x=0.25m[/tex].
Thus the spring constant:
[tex]k=\frac{18N}{0.25m}[/tex]
[tex]k=72N/m[/tex]
And now we do have everything necessary to calculate the angular frequency:
[tex]\omega=\sqrt{\frac{k}{m} }=\sqrt{\frac{72N/m}{2kg} }=\sqrt{36}[/tex]
[tex]\omega=6rad/s[/tex]
the angular frequency of the oscillation is 6 rad/s
