A typical solution of an overdamped system with periodic external lorces is ol t

Question

A typical solution of an overdamped system with periodic external lorces is ol the form O a(t) e cos(t) +sin(t). O a(t) +sin(t) O ar sin (2t) +cos(3t) O r(t)- sin (t). The Laplace transform of a polynomial is O a rational function. O a polynomial. an exponential function. O a trigonometric function. 0, then its Laplace for all t f(t) satisfies lf() If a smooth function transform is guaranteed to exist for O s 0. O s 0. O s 10. O s 2 10. The solutions to the equation r' r" are O a vector space of dimension 1. O a vector space of dimension 2. O infinitely many but not a vector space. O finitely many. The equation 2r" 3r' r cos (t) describes O underdamped oscillations. O overdamped oscillations. O critically damped oscillations. o undamped oscillations

Explanation / Answer

1) tsint--> since overdamped condition the function is not decaying

2) is a rational function as laplace of tn is n!/(sn+1)

3) s>10

4) vector space of dimension 2

5) overdamped system as discrimination of homogenous solution is greater than 0

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