The discussion focuses on the analysis of undamped harmonic motion of a mass attached to a rod with a stationary bushing. The mass experiences a vertical motion defined by y(t) = 0.4 sin(20t) cm, leading to a derived acceleration a(t) = -160 sin(20t) cm/s². Participants clarify that the rod's deflection of 2 cm indicates its properties, and the problem requires finding the periodic steady-state solution without needing additional initial conditions. The net force on the mass is expressed as ΣF = m(x'' - 1.6 sin(20t)) = -kx - mg, where k is the spring constant derived from the rod's deflection.
PREREQUISITESStudents and professionals in mechanical engineering, physics, and applied mathematics who are working on problems related to harmonic motion and structural dynamics.
No, that only works at t=0. Over time, the average of that sum of trig functions is zero, not -mg/k.Feodalherren said:Or acutally, couldn't I just find that with
x(0)=-mg/k= [(P/k) / (1-(Wn/Ω)^2)]sin(Ωt) + Acos(Wn*t) + Bsin(Wn*t)
so
A=-mg/k
No, you have two. At time zero it is at rest in the equilibrium position.Feodalherren said:So then by the principle of superpositioning it should be
x(t)= [(P/k) / (1-(Wn/Ω)^2)]sin(Ωt) + Acos(Wn*t) + Bsin(Wn*t) - mg/k
but then I arrive back at my original issue - how do I find A and B. I only have one initial condition?