As the robotic arm moves to pick up components, it encounters friction and damping effects. The motion of the robotic arm is governed by the equation: d²x m dr² + dx dt +kx F(t) where x is the displacement, m is the mass, c is the damping coefficient, k is the spring constant, and Ft) is the external force. Solve this equation for x(t) if m-2 kg, c=0.5 Ns/m, k=3 N/m for the following cases below case 1: when F (t)=0 and case 2: when Rt)=4sin(2t) N.
As the robotic arm moves to pick up components, it encounters friction and damping effects. The motion of the robotic arm is governed by the equation: d²x m dr² + dx dt +kx F(t) where x is the displacement, m is the mass, c is the damping coefficient, k is the spring constant, and Ft) is the external force. Solve this equation for x(t) if m-2 kg, c=0.5 Ns/m, k=3 N/m for the following cases below case 1: when F (t)=0 and case 2: when Rt)=4sin(2t) N.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:As the robotic arm moves to pick up components, it encounters friction and damping
effects. The motion of the robotic arm is governed by the equation:
d²x
m
dr²
+
dx
dt
+kx
F(t) where x is the displacement, m is the mass, c is the damping
coefficient, k is the spring constant, and Ft) is the external force. Solve this equation for
x(t) if m-2 kg, c=0.5 Ns/m, k=3 N/m for the following cases below
case 1: when F (t)=0 and case 2: when Rt)=4sin(2t) N.
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