Please solve the following question:
The energy of a system as a function of time t...(Please find full question in image.)

Asked by kirthanps | 22nd Nov, 2020, 12:27: PM

Expert Answer:

Energy of system at time t , E(t) = A2 exp( -α t )  .................(1)
 
where α = 0.2 s-1 is constant 
 
By taking logarithm on both side of eqn.(1) , we get ,  ln [ E(t) ] = 2 ln(A) - α t  ............(2)
 
By differentiating eqn.(2) , we get , ( dE/E ) = 2 (dA/A) - α dt .............(3)
 
we are given that ,  (dA/A ) × 100 = 1.5 %   , i.e., dA/A = 0.015 ................(4)
 
(dt/t) × 100 = 1.25 % , i.e., dt/t = 0.0125   ...................(5)
 
Hence from eqn.(3) , we get at t= 5 s,  ( dE/E )  = 2 × 0.015 + 0.2 × ( .0125 *5 ) =  0.0425
 
( error is always added together , hence - α dt is considered as + α dt  in above calculation.
We can consder error in time ±dt , hence -ve sign is considered  for dt to get maximum error possible)
 
Hence percentage error in E at t= 5 s is 4.25 %

Answered by Thiyagarajan K | 22nd Nov, 2020, 02:10: PM

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