Pendulum Dangling from a Slider-Crank

start-reset

pendulum

initial angular position

θ

0

-1.

mass of bob m

1

damping coefficient μ

0.1

crank-slider drive

crank arm length r

0.35

connecting rod length s

1.5

crank speed ω

7.1

This Demonstration shows the motion of a pendulum dangling from the end of a horizontal slider-crank.

The equation of motion is

gmsin(θ(t))+mx''(t)cos(θ(t))+mℓθ''(t)+μℓ(θ'(t)+x'(t)cos(θ(t)))0

; it expresses the equilibrium of the four forces acting on the pendulum bob: gravity, centrifugal force, the force resulting from the horizontal acceleration transmitted from the slider-crank, and the damping force.