We know that the time period for an oscillating magnet is given by:
T=2π√‌where:
M is the magnetic moment,
I is the moment of inertia, and
BH is the horizontal component of the Earth's magnetic field.
Given that the magnetic moment decreases by
19%, we can express the initial magnetic moment as
M1=m and the reduced magnetic moment as:
M2=m−‌=0.81mFrom the equation for the time period, we derive:
‌=√‌Substituting the values we have:
‌=√‌=√0.81=‌Rearranging gives:
T2=‌T1This implies:
T2=1.11T1So, the new time period
T2 is
T1+0.11T1, which indicates that:
The time period increases by
11%.