mathcad: help with Numerical Soln to Differential Eqn
Please help to implement following differential equation numerical solution in mathcad
Numerical solution for single degree of freedom elastic system.
Spring stiffness = k = 2000 lbf/ft
Weight = W = 64 lbf
Force function:
F(t) = 500t+50 if t <=0.1
=-1250t+225 if 0.1 <=t<= 0.14
= 50 if t>=0.14
Acceleration function:
A(t) = ½ F(t) – 1000 *Y
Say time step = dt = 0.02
Initial Condition:
Displacement:
Y0 = 0 that is displacement is zero when t = 0
Y1 = ½ * A0 *dt^2 that is first time step which t = 0.02 this gives displacement but in terms of Acceleration at t =
Acceleration:
A0 = 0 when t = 0
Solution:
Y (t+dt) = 2 * Y (t) – Y(t-dt) + A(t) * dt^2
For t – 0 to 0.4 with dt = 0.02
Return:
Y, A

