The time period of oscillation of a freely suspended bar magnet with usual notations is given by

Two different magnets are tied together and allowed to vibrate in a horizontal plane. When their like poles are joined,the time period of oscillation is $5 \, s$,and when their unlike poles are joined,the time period of oscillation is $15 \, s$. The ratio of their magnetic moments is

$A$ vibration magnetometer is placed at the south pole; then its time period will be

Two magnets are held together in a vibration magnetometer and are allowed to oscillate in the Earth's magnetic field. With like poles of magnets together,$12$ oscillations per minute are made,but for unlike poles together,only $4$ oscillations per minute are executed. The ratio of their magnetic moments is

$A$ short bar magnet having a magnetic moment $4 \text{ Am}^2$,placed in a vibrating magnetometer,vibrates with a time period of $8 \text{ s}$. Another short bar magnet having a magnetic moment $8 \text{ Am}^2$ vibrates with a time period of $6 \text{ s}$. If the moment of inertia of the second magnet is $9 \times 10^{-2} \text{ kg-m}^2$,the moment of inertia of the first magnet is (assume that both magnets are kept in the same uniform magnetic induction field).

$A$ bar magnet is oscillating in the Earth's magnetic field with a period $T$. What happens to its period and motion if its mass is quadrupled?