Final answer:
The bandwidth of the system with the transfer function G(s) = 4/(0.2s + 1) is 5 rad/s, which is the same as its cutoff frequency.
Step-by-step explanation:
The bandwidth of the system represented by the transfer function G(s) = 4/(0.2s + 1) can be determined from the denominator of the transfer function. The bandwidth is typically defined as the range of frequencies over which the response of the system is above a certain relative level (commonly 3 dB below the peak value). In this case, the transfer function corresponds to a first-order system, where the bandwidth is the same as the cutoff frequency. The cutoff frequency ωc is the value of s at which the magnitude of the transfer function is −1/−σ dB down from its zero-frequency value. For the standard form of a first-order system G(s) = 1/(Ts + 1), the bandwidth or cutoff frequency is ωc = 1/T. Comparing this with the given G(s), T is 0.2, hence ωc = 1/0.2 = 5 rad/s. Therefore, the bandwidth of the system is 5 rad/s.