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Solved Problems-3

Problems-3
Consider the system S whose input and output are related by,
 
y(t) = x2(t)
 
Check whether S is linear.
Solution
For an input x1(t), output, y1(t) = x12(t)
 
For an input x2(t), output, y2(t) = x22(t)
 
For an input {k1x1(t) + k2x2(t)}, output, y3(t) = Description: Description: Description: 2607.png …(i)
 
where, k1 and k2 are any arbitrary constants.
 
From the condition of linearity, the output should be
 
{k1y1(t) + k2y2(t)} = k1x12(t) + k2x22(t) …(ii)
 
From equations (i) and (ii), we conclude that the system is not linear.
 




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