An uncharged capacitor C = 4.7 µF is charged from a 12 V step source through a resistor R = 47 kΩ. How long after closing the switch does the capacitor voltage reach 99 % of its final value? Find t in ms.
A first-order system G(s) = 10/(s + 2) receives a step input of size 5 at t = 0, starting from rest. Find the final value y(∞) of the output.
A system has the transfer function G(s) = 166/(s² + 10s + 83) and receives a unit step input. Find the peak time tp of the step response.
A system has the transfer function G(s) = 24.5/(s² + 11s + 49) and receives a unit step input. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).
A mass m = 2 kg hangs on a spring k = 2000 N/m with a viscous damper c = 63 N·s/m (m·x″ + c·x′ + k·x = F). At rest in equilibrium, a constant force F = 20 N is suddenly applied. Find the percent overshoot %OS of the displacement.
A mass m = 10 kg hangs on a spring k = 5000 N/m with a viscous damper c = 89 N·s/m (m·x″ + c·x′ + k·x = F). At rest in equilibrium, a constant force F = 20 N is suddenly applied. Find the largest displacement xmax in mm.
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