two light identical springs of spring constant K are attached horizontally at the two ends of a uniform horizontal rod AB of length l and mass m. the rod is pivoted at its centre 'o' and can rotate freely in horizontal plane . The other ends of the two springs are fixed to rigid supportss as shown in figure . the rod is gently pushed through a small angle and released , the frequency of resulting oscillation is :

A homogenous rod XY of length L and mass 'M' is pivoted at the centre 'C' such that it can rotate freely in vertical plane. Initially the rod is in the horizontal position.

The arrangement shown of a uniform rod of length l and mass m, pivoted at the centre and its two ends attached to two springs of spring constant K_(1) and K_(2) . The other end of springs are fixed to two rigid supports the rod which is free to rotate in the horizontal plane , is pushed by a small angle in one direction and released . Teh frequency of oscillation of the rod is

A uniform rod of length L and mass M is pivotedat the centre. Its two ends are attached to two springs of equal spring constants. k . The springs as shown in the figure, and the rod is free to oscillate in hte horizontal plane. the rod is gently pushed through a small angle theta in one direction and released. the frequency of oscilllation is-

A uniform rod of length l and mass M is pivoted at the centre. Its two ends are attached to two ends are attached to two springs of equal spring constant k. the springs are fixed to rigid support as shown in figure and the rod is free to oscillate in the horizontal plane. the rod is gently pushed through a small angle theta in one direction and released. the frequency of oscillation is

A uniform rod of length l and mass M is pivoted at the centre. Its two ends are attached to two ends are attached to two springs of equal spring constant k. the springs are fixed to rigid ruppot as shown in figure and the rod is free to oscillate in the horizontal plane. the rod is gently pushed through a small angle theta in one direction and relased. the frequency of oscillation is

A uniform rod of length (L) and mass (M) is pivoted at the centre. Its two ends are attached to two springs of equal spring constants (k). The springs are fixed to rigid supports as shown in the figure, and the rod is free to oscillate in the horizontal plane. The rod is free to oscillate in the horizontal plane. The rod is gently pushed through a small angle (theta) in one direction and released. The frequency of oscillation is. ? (##JMA_CHMO_C10_009_Q01##).

A straight rod of light L and mass m is pivoted freely from a point of the roof. Its lower end is connected to an ideal spring of spring constant K. The other end of the spring is connected to the wall as shown in the figure. Find the frequency of small oscillation of the system.

A ring of mass m is attached to a horizontal spring of spring constant k and natural length l_0 . The other end of the spring is fixed and the ring can slide on a horizontal rod as shown. Now the ring is shifted to position B and released Find the speed of the ring when the spring attains its natural length.