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The step response of the system is c(t) = 10+8e-t-4/8e-2t . The gain in time constant form of transfer function will be: 
  • a)
    -7
  • b)
    7
  • c)
    7.5
  • d)
    -7.5
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The step response of the system is c(t) = 10+8e-t-4/8e-2t. The gain in...
Differentiating the equation and getting the impulse response and then taking the inverse Laplace transform and converting the form into time constant form we get K = -7.5.
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Most Upvoted Answer
The step response of the system is c(t) = 10+8e-t-4/8e-2t. The gain in...
The given step response of the system is represented by the equation c(t) = 10 8e-t-4/8e-2t. From this equation, we can see that the step response can be written in time constant form as c(t) = K(1 - e^(-t/T))/(1 - e^(-t/2T)), where K is the gain and T is the time constant.

To find the gain in time constant form of the transfer function, we need to determine the value of K. By comparing the given step response equation with the time constant form equation, we can see that K = 10 8 and T = 2.

Therefore, the gain in time constant form of the transfer function is K/T = 10 8 / 2 = -7.5.

Hence, the correct answer is option 'D', -7.5.
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