Question

10. /1 points Zill DiffEQModAp11 7.3.057 Write the function in terms of unit step functions. Find the Laplace transform of the given function. t2 F(s) - Need Help? Read It Talk to a Tutor Submit Answer Save Progress 11. -/1 points ZillDiffEQModAp11 7.3.059 Write the function in terms of unit step functions. Find the Laplace transform of the given function. 0, t2 9 F(s) Need Help? Read It Talk to a Tutor

Answer 1

We have u (t) = {0 t < 0 1 t greaterthanorequalto 0 since current function remain positive only between 0 89 It can be written as f (t) = t [u (t) - u (t - g)] Now, we know, L (u (t - a) f (t - a)) = e^-as F (s) where F (s) = L (f (t)) - (1) L (u (t) t) = e^-0s (1/s^2) = 1/s^2 - from (1) L (u (t - g) t) = L (u (t - g) (t - g + g)) = e^-9s L ((t)) where g (t) = t + g = e^-9s G (s) G (s) = 1/s^2 + 9/s = e^-9s (1/s^2 + 9/s) \r\n f (t) = t [u (t) - u (t - 9)] f (t) = t u (t) - t u (t - 9) L [f (t)] = L [t u (t)] - L [t u (t - 9)] = 1/s^2 - e^9s (1/s^2 + 9/s)