D

Step 1: Understand the principles of a vibration magnetometer. A vibration magnetometer typically oscillates in a magnetic field. The period of oscillation is influenced by several physical parameters.

Step 2: Identify the variables:
- I: Current flowing through the coil (which generates a magnetic field)
- M: Magnetic moment of the magnet used in the device
- H: Magnitude of the external magnetic field

Step 3: Analyze how each parameter affects the period of oscillation. The formula for the period of oscillation (T) of a magnetic dipole in a magnetic field is given by:
$$ T = 2eta rac{ ext{I} ext{M}}{ ext{H}} $$
From the formula, it is clear that the period T is directly dependent on the magnetic moment M and current I, and inversely dependent on the external magnetic field H. Therefore, variations in any of these parameters will affect the period.

Step 4: Conclude that all three factors (I, M, and H) influence the period of oscillation.
Therefore, the correct answer is D: I, M, and H only.