Explanation:
To solve this problem, we need to understand the concept of damping in a harmonic oscillator and how energy is lost over time.

Damped Harmonic Oscillator:
A damped harmonic oscillator is a system that experiences a resistive force as it oscillates. This resistive force, known as damping, causes the amplitude of the oscillator to decrease over time. The equation of motion for a damped harmonic oscillator is given by:

m*d^2x/dt^2 + b*dx/dt + k*x = 0

Where:
m is the mass of the oscillator
x is the displacement of the oscillator from its equilibrium position
t is time
b is the damping constant
k is the spring constant

Energy Loss:
The energy of a harmonic oscillator can be expressed as the sum of its kinetic and potential energies:

E = (1/2)k*x^2 + (1/2)m*v^2

Where:
E is the total energy of the oscillator
v is the velocity of the oscillator

The rate of change of energy with respect to time is given by:

dE/dt = -b*dx/dt

This equation tells us that the rate of energy loss is proportional to the damping constant and the rate of change of displacement with respect to time.

Rate of Energy Loss:
In this problem, it is given that the oscillator loses energy at a rate of 4% per minute. Mathematically, this can be written as:

dE/dt = -0.04E

By substituting the expression for dE/dt from above, we get:

-0.04E = -b*dx/dt

This equation relates the rate of energy loss to the rate of change of displacement with respect to time.

Relation between Amplitude and Energy:
The amplitude of the oscillator is related to its energy. In a harmonic oscillator, the maximum displacement from the equilibrium position is equal to the amplitude of the oscillation. Therefore, as the oscillator loses energy, the amplitude decreases over time.

Calculating the Decrease in Amplitude:
We are asked to find the decrease in amplitude per minute. Since the amplitude is directly proportional to the energy, we can conclude that the decrease in amplitude per minute will be the same as the decrease in energy per minute.

From the equation -0.04E = -b*dx/dt, we can see that the decrease in energy per minute is equal to 0.04E. Therefore, the decrease in amplitude per minute will also be 4%.

However, it is important to note that the question asks for the closest value. The closest value to 4% among the given options is 2%. Therefore, the correct answer is 2%.