Period of oscillation of dip needle

Amith2006

1)The time period of a dip needle vibrating in the vertical plane in the magnetic meridian is 3 seconds. When the same magnetic needle is made to vibrate in the horizontal plane, the time period of vibration is 3(2)^(1/2). What is the angle of dip of the place?
I think in both the cases, it is the horizontal component of earth’s magnetic field that exerts a restoring couple on the dip needle and causes it to oscillate. But how to go further?Please give an idea on how to solve this problem.

OlderDan

My interpretation: When the needle is in the vertical plane in the magnetic meridian it should be free to align with the full magnetic field. When it is horizontal, it can only align with the horizontal component.

Amith2006

That's great!Thanks.