Crey | Consider the system shown in the figure. A rope goes over a pulley. A mass, 𝒎, is hanging from the rope. A spring of stiffness, k, is attached at one end of the rope. Assume rope is inextensible, massless and there is no slip between pulley and rope. The pulley radius is 𝒓 and its mass moment of inertia is 𝑱. Assume that the mass is vibrating harmonically about its static equilibrium position. The natural frequency of the system is k r 2 J + m r 2 , k / m , k r 2 J − m r 2 , k r 2 J

Question

Consider the system shown in the figure. A rope goes over a pulley. A mass, 𝒎, is hanging from the rope. A spring of stiffness, k, is attached at one end of the rope. Assume rope is inextensible, massless and there is no slip between pulley and rope.

The pulley radius is 𝒓 and its mass moment of inertia is 𝑱. Assume that the mass is vibrating harmonically about its static equilibrium position. The natural frequency of the system is

Options :

$\sqrt{\frac{k r^{2}}{J + m r^{2}}}$
$\sqrt{k / m}$
$\sqrt{\frac{k r^{2}}{J - m r^{2}}}$
$\sqrt{\frac{k r^{2}}{J}}$

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