Question

1. Linearity and Time Invariance of Systems (a) $y = 3u$ (b) $y(t) = u(t)$ (c) $y(t) = u^2(t)$ (d) $y(t) = 2e^{-3t}u(t - T)$ (e) $y(t) = 3u(t - 2)$ (f) $y(t) = \int_{-\infty}^{t} u(\tau)d\tau$ (g) $y(t) = 3 \int_{-\infty}^{t} \tau u(\tau) d\tau$ (h) $y(t) = 5 \int_{-\infty}^{t} u^2(\tau) d\tau$ (i) $y(t) = x_0e^{-t} + \int_{t_0}^{t} e^{\tau - t}u(\tau) d\tau$ For each of the systems above, determine conclusively whether it is: (i) linear, (ii) time-invariant,

          1. Linearity and Time Invariance of Systems
(a) $y = 3u$
(b) $y(t) = u(t)$
(c) $y(t) = u^2(t)$
(d) $y(t) = 2e^{-3t}u(t - T)$
(e) $y(t) = 3u(t - 2)$
(f) $y(t) = \int_{-\infty}^{t} u(\tau)d\tau$
(g) $y(t) = 3 \int_{-\infty}^{t} \tau u(\tau) d\tau$
(h) $y(t) = 5 \int_{-\infty}^{t} u^2(\tau) d\tau$
(i) $y(t) = x_0e^{-t} + \int_{t_0}^{t} e^{\tau - t}u(\tau) d\tau$
For each of the systems above, determine conclusively whether it is:
(i) linear,
(ii) time-invariant,

1. Linearity and Time Invariance of Systems
(a) y = 3u
(b) y(t) = u(t)
(c) y(t) = u^2(t)
(d) y(t) = 2e^-3tu(t - T)
(e) y(t) = 3u(t - 2)
(f) y(t) = ∫-∞^t u(τ)dτ
(g) y(t) = 3 ∫-∞^tτ u(τ) dτ
(h) y(t) = 5 ∫-∞^t u^2(τ) dτ
(i) y(t) = x0e^-t + ∫t0^t e^τ - tu(τ) dτ
For each of the systems above, determine conclusively whether it is:
(i) linear,
(ii) time-invariant,

Added by Erik B.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Thanks for your feedback!

Linearity and Time Invariance of Systems (a) y=3u (b) y(t)=u(t) (c) y(t)=u^(2)(t) (d) y(t)=2e^(-3t)u(t-T) (e) y(t)=3u(t-2) (f) y(t)=int_(-infty )^t u( au )d au (g) y(t)=3int_(-infty )^t au u( au )d au (h) y(t)=5int_(-infty )^t u^(2)( au )d au (i) y(t)=x_(0)e^(t_(0)-t)+int_(t_(0))^t e^( au -t)u( au )d au For each of the systems above, determine conclusively whether it is: (i) linear, (ii) time-invariant Please write the answer in math equation for each question, thank you. 1. Linearity and Time Invariance of Systems (a) y=3u (b)y(t)=u(t) (c)y(t=u2t) (d) y(t)=2e-3tu(t-T) (e) y(t) =3u(t -2) (f)y(t)=fu(T)dT (g) y(t)=3 f_ Tu(T) dT (h) y(t)=5 f-u2(T)dr For each of the systems above, determine conclusively whether it is: (i) linear, (ii) time-invariant,