Number 2 1. a) The displacement x of a forced spring-mass system is governed by dx…

Number 2
1. a) The displacement x of a forced spring-mass system is governed by dx d2x dt2 + (1 + t)x2 = sint t> 0 x(0) = 0 dx (0) = 0 dt dt Obtain the first four non-zero terms of the solution using the Taylor expansion approach. b) Calculate the position and velocity of the mass at t = 0.5 using the result of part (a). a) The displacement x of a forced spring-mass system is governed by them to a + (1 + t)x? = sint dx t> 0 x(0) = 0 0) = 0 dt Obtain the first four non-zero terms of the solution using the Taylor expansion approach. b) Calculate the position and velocity of the mass at t = 0.5 using the result of part (a). 2. Obtain the position and velocity of the mass in problem (1) at t = 0.5 using the Modified Euler’s Method (Midpoint Method) with a step size of 0.25.