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The system represented by equation—
(i) y(t) = 5 sin x(t)
(ii) y(t) = 7x(t) + 5
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- (i) is linear, (ii) is non-linear
- (i) is non-linear, (ii) is linear
- Both (i) and (ii) are linear
- Both (i) and (ii) are non-linear
Correct Option: D
(i) y(t) = 5 sin x(t)
F[x1(t)] = y1(t) = 5 sin x1(t)
F[x2(t)] = y2(t) = 5 sin x2(t)
F[x1(t)] + F[x2(t)] = 5[sin x1(t) + sin x2(t)]}
whereas,F[x1(t) + x2(t)] = 5{sin [x1(t) + x2(t)}]
Since here,
F[x1(t) + F] [x2(t)] ≠ F[x1(t) + F[x2(t)]
and hence the system is non-linear.
(ii) y(t)=7x(t) + 5
F[x1(t)] = y1(t) = 7x1(t) + 5
F[x2(t)] = y2(t) = 7x2(t) + 5
Therefore,
F[x1(t)] + F[x2(t)] = 7[x1(t) + x2(t)] + 0
where, F[x1(t) +x2(t)] = 7[x1(t) + x2(t)] + 5
Since here,
F[x1(t) +x2(t)] ≠ F[x1(t) + F[x2(t)]
Hence, the system is non-linear.
Hence, alternative (D) is correct choice.
