The given equation for the simple harmonic motion (SHM) is x = 0.05 cos(100t - 3π/4) meters. We need to find the frequency of oscillation, initial phase, maximum velocity, and total energy.

1. Frequency of Oscillation:
The equation for the displacement of a particle executing SHM is given by x = A cos(ωt + φ), where A is the amplitude, ω is the angular frequency, t is time, and φ is the phase angle.

Comparing the given equation with the general equation, we can see that the angular frequency ω = 100 rad/s. The frequency of oscillation (f) is related to the angular frequency by the equation f = ω/(2π).

Therefore, the frequency of oscillation is f = 100/(2π) ≈ 15.92 Hz.

2. Initial Phase:
The initial phase (φ) is the phase angle when t = 0. From the given equation, we can see that the phase angle is -3π/4.

Therefore, the initial phase is φ = -3π/4 radians.

3. Maximum Velocity:
The velocity of a particle executing SHM is given by v = -Aω sin(ωt + φ).

To find the maximum velocity, we need to find the maximum value of the absolute value of v. The maximum value of the absolute value of sin function is 1.

Therefore, the maximum velocity is vmax = Aω = 0.05 * 100 = 5 m/s.

4. Total Energy:
The total energy (E) of a particle executing SHM is the sum of its kinetic energy (K) and potential energy (U). The equation for total energy is E = K + U.

The kinetic energy of the particle is given by K = (1/2)mv^2, where m is the mass of the body and v is the velocity.

The potential energy of the particle is given by U = (1/2)kx^2, where k is the spring constant and x is the displacement.

In this case, there is no mention of the spring constant or any information about the force acting on the body. Therefore, we cannot calculate the spring constant or the potential energy. Hence, we cannot calculate the total energy.

To summarize:
1. The frequency of oscillation is approximately 15.92 Hz.
2. The initial phase is -3π/4 radians.
3. The maximum velocity is 5 m/s.
4. The total energy cannot be calculated without information about the spring constant or potential energy.