Find the second order derivative of sin(x^2)
First order derivative = 2xcos(x^2) Second order derivative = -4xsin(x^2)
Find the Laplace transform of ((t^2) + (e^2)(sin2t))
Use the general table to find t^2 Solution: n!/s^(n+1) Where n is t^n =2!/s^(2+1) =2/s^3 Use S-Shifting (First translation theorem to find (e^2)(sin2t)) Side note: We know to use s shifting due to observing that there is an exponential function (e^2) being multiplied by another function (sin2t) We can use the general formulation of S-Shifting to solve this. First step: We need f(s-a) = F(s) and a is found in e^a and in this case, it is 2 Second Step: Find the general formulation of the Laplace of Sin2t which is k/s^2 + k^2 where k is Sinkt in the formula The Laplace of sin2t is 2/s^2 + 2^2 = 2/(s)^2+4 a = 2 F(s-2) = 2/(s)^2 +4 Now substitute F(s) = 2/(s+2)^2 + 4
What is beam design governed by?
1) Moment, where the resistance must be greater than the failure 2) Shear 3) Deflection, where the actual deflection must be greater than the limit