1. The problem statement, all variables and given/known data "If a horizontal force of F = 299kN is applied to the right at the girder level by a hydraulic jack and then the force is removed suddenly, find the equation of motion of the girder. Consider 5% critical damping. Find the displacement and velocity of the girder at 0.2 seconds after release of the force." This is of a braced single storey building. (bottom left is braced to top right etc) I = 7.6*10^6mm^4 E = 200 GPa Length of Girder = 6m Height of Columns = 3.5m The braced bars are 25mm diameter. This meant that the Area of them came to 490.874mm^2 as Area = (pi*d^2) / 4 mass of frame = 4000kg. stiffness (girder and two columns) = 11404.775N/mm natural frequency = 53.4 rad/s 2. Relevant equations m*(acceleration) + c*velocity +k*displacement = F(x) -> (Inertia Force + Viscous force + Stiffness force = F(x)) critical damping constant = 2*mass*omega damped natural frequency = natural frequency * sqrt (1-ξ^2) natural frequency = sqrt (stiffness / mass) 3. The attempt at a solution I calculated Stiffness in both the columns and the rigid girder. This came to 11404.775. I solved for the columns by using (12EI/L^3) multiplied by 2 as there are two columns. For the rigid girder, I had to take into account theta. I then calculated natural frequency of vibration after finding stiffness and dividing it out by the mass. After square rooting the fraction, it came to 53.4 rad/sec. I then calculated the critical damping constant, this came to 427200kg/sec as critical damping constant Cc = 2*mass*natural frequency. C actually was less than Cc, meaning it is under critically damped. ξ = 0.05. I then went back to m*(acceleration) + c*velocity +k*displacement = F(x) I then made all of it equal to zero, deriving from a characteristic equation and then solving for the roots using the quadratic formula. All this did was bring me back to an equation I already knew from my notes, as shown with attached image. I am wondering, since it is applied instantaneously, does m*acceleration + c*velocity + k*displacement still equal to 0? or does it equal to 299kN?? The 299 is throwing me off because I was told if the frame is free moving, then it should equal to zero. Also I'm not sure about writing the equation of motion when I am not given the initial velocity or displacement constraints. Apologies if this question sounds a bit silly - I haven't come across one of these questions in my tutes!