Answer:
Explanation:
Given
[tex]\rho _c=[/tex]density of cork
[tex]\rho _w=[/tex]density of water
L=Length of cylinder
If initially x length is under water
At equilibrium
[tex]\rho _wAxg-\rho _cALg=0[/tex]
After giving [tex]X_m[/tex] push
[tex]\rho _wAg(x+X_m)-\rho _cALg=\rho _cALa[/tex]
where a is acceleration of system
and [tex]a=\frac{\mathrm{d^2} X_m}{\mathrm{d} t^2}[/tex]
[tex]\rho _wAgX_m=\rho _cAL\frac{\mathrm{d^2} X_m}{\mathrm{d} t^2}[/tex]
[tex]\frac{\mathrm{d^2} X_m}{\mathrm{d} t^2}=\frac{\rho _wAg}{\rho _cAL}[/tex]
thus [tex]\omega ^2=\frac{\rho _wg}{\rho _cL}[/tex]
thus [tex]\omega =\sqrt{\frac{\rho _wg}{\rho _cL}}[/tex]
and [tex]2\pi f=\omega [/tex]
[tex]f=\frac{\sqrt{\frac{\rho _wg}{\rho _cL}}}{2\pi }[/tex]
