An uncharged capacitor C = 4.7 µF is charged from a 10 V step source through a resistor R = 47 kΩ. How long after closing the switch does the capacitor voltage reach 98 % of its final value? Find t in ms.
A first-order system G(s) = 2.5/(0.5s + 1) receives a step input of size 1 at t = 0, starting from rest. Find the final value y(∞) of the output.
A system has the transfer function G(s) = 58/(s² + 10s + 58) and receives a unit step input. Find the peak time tp of the step response.
A system has the transfer function G(s) = 27.5/(s² + 6s + 55) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.
A mass m = 0.5 kg hangs on a spring k = 1000 N/m with a viscous damper c = 22 N·s/m (m·x″ + c·x′ + k·x = F). At rest in equilibrium, a constant force F = 50 N is suddenly applied. Find the largest displacement xmax in mm.
The step response of a second-order system without zeros shows 5 % overshoot, and the first peak occurs at t = 0.1 s. Find the natural frequency ωn.
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