Forward Path Transfer Function:
The forward path transfer function of the system is given by G(s) = 100/(s^2 + 10s + 100).

Frequency Response:
The frequency response of a system is the output of the system when a sinusoidal input signal is applied at different frequencies. It provides information about how the system responds to different frequencies.

Resonance Peak:
The resonance peak is the maximum value of the frequency response. It occurs at the resonant frequency, which is the frequency at which the system output is maximum.

Calculating Resonant Frequency:
To find the resonant frequency, we need to determine the frequency at which the magnitude of the frequency response is maximum.

Magnitude of the Frequency Response:
The magnitude of the frequency response is given by |G(jω)|, where ω is the frequency.

Substituting jω for s in the forward path transfer function, we get:
G(jω) = 100/((jω)^2 + 10(jω) + 100)
= 100/(-ω^2 + j10ω + 100)

Calculating Magnitude:
To calculate the magnitude of the frequency response, we need to find |G(jω)|.

|G(jω)| = sqrt(Re(G(jω))^2 + Im(G(jω))^2)

For a complex number G(jω) = a + jb, where a is the real part and b is the imaginary part, the magnitude is given by |G(jω)| = sqrt(a^2 + b^2).

So, in our case, we have:
|G(jω)| = sqrt((-ω^2)^2 + (10ω)^2 + 100^2)
= sqrt(ω^4 + 100ω^2 + 10000)

Finding Maximum Magnitude:
To find the maximum magnitude, we can differentiate the magnitude equation with respect to ω and equate it to zero.

d(|G(jω)|)/d(ω) = 0

Differentiating the magnitude equation, we get:
2ω^3 + 200ω = 0

Simplifying the equation, we have:
ω(ω^2 + 100) = 0

So, the possible values of ω are ω = 0 and ω = sqrt(-100).

Since ω cannot be a negative value, the only possible value is ω = 0.

Resonant Frequency:
The resonant frequency is the non-zero value of ω that maximizes the magnitude of the frequency response.

Therefore, the resonant frequency is ω = 0.

Converting to Rad/Sec:
In the given options, the frequencies are given in rad/sec. The resonant frequency in rad/sec is obtained by multiplying the resonant frequency in Hz by 2π.

ω_rad/sec = ω_Hz * 2π

Since the resonant frequency is ω = 0, the resonant frequency in rad/sec is 0 rad/sec.

Conclusion:
Therefore, the frequency response of the system will exhibit the resonance peak at 0 rad/sec. None of the given options (a, b, c, d) are correct.