Question

Problem #1: Consider the following statements. [6 marks] (i) Spring/mass systems and Series Circuit systems we covered are examples of linear dynamical systems in which each mathematical model is a second-order constant coefficient ODE along with initial conditions at a specific time. (ii) The following is an example of a piece-wise continuous function f(x) = {* terie (iii) It is unclear whether series solutions to ODEs even exist, and knowing about series solutions to ODEs is mostly irrelevant in applications. (iv) It is necessary for a function to be of exponential order in order for its Laplace Transform to be defined for some values of s. (v) There is a systematic way of computing solutions to homogeneous second-order linear constant coefficient ODES. (vi) There is only one way to compute the Laplace Transform of an arbitrary piece-wise continuous, but not continuous, function. Determine which of the above statements are True (1) or False (2). So, for example, if you think that the answers, in the above order, are True False,False,True False,True then you would enter '1,2,2,1,2,1' into the answer box below (without the quotes).

Consider the following statements. (i) Spring/mass systems and Series Circuit systems we covered are examples of linear dynamical systems in which each mathematical model is a second-order constant coefficient ODE along with initial conditions at a specific time. (ii) The following is an example of a piece-wise continuous function f (x)  = { x x ∈ Q 0 x ∈ R \ Q (iii) It is unclear whether series solutions to ODEs even exist, and knowing about series solutions to ODEs is mostly irrelevant in applications. (iv) It is necessary for a function to be of exponential order in order for its Laplace Transform to be defined for some values of s. (v) There is a systematic way of computing solutions to homogeneous second-order linear constant coefficient ODEs. (vi) There is only one way to compute the Laplace Transform of an arbitrary piece-wise continuous, but not continuous, function. Determine which of the above statements are True (1) or False (2). So, for example, if you think that the answers, in the above order, are True,False,False,True,False,True then you would enter '1,2,2,1,2,1' into the answer box below (without the quotes).

Answer 1