Formulas used in the experiment

• Characteristic equation is given by : s² + 2ζω_ns + ω_n²=0


• Natural frequency : ω_n = √(coefficient of constant term)


• Damping ratio : ζ = (coefficient of s¹)/2w_n


• Settling time : t_s = 4/ζ*ω_n


• Peak time : t_{p =} π/ω_n* √(1-ζ²)


• Rise time : t_{r =} π-Φ/ω_n* √(1-ζ²) where Φ = tan^-1√((1-ζ²)/ζ)


• Delay time : t_{d =} (1+(.7*ζ))/ω_n


• Maximum overshoot : M_pe^{-(ζ*π)/(√(1-ζ2))}

Enter the coefficients of characteristic equation

Result

c(t) = u(t) - e^-ζω_ntcosω_dtu(t) - (ζω_n/ω_d)e^-ζω_ntsinω_dtu(t)
c(t) = 1 - cosω_n
c(t) = (1 - e^-ω_nt - ω_nte^-ω_nt)u(t)
c(t) = u(t) + Ce^{-(ζω_n-ω_n√(ζ2-1))t}u(t)






Click the following button to get the time domain specifications

Time domain specifications

System Parameters