# SolSec1.8 - Problems and Solutions Section 1.8 (1.80...

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Problems and Solutions Section 1.8 (1.80 through 1.82) 1.80 Consider the inverted pendulum of Figure 1.36 as discussed in Example 1.8.1. Assume that a dashpot (of damping rate c ) also acts on the pendulum parallel to the two springs. How does this affect the stability properties of the pendulum? Solution: The equation of motion is found from the following FBD: m l c k k 0 θ F dash mg 2 F sp + Moment about O: Σ MI o = ˙˙ θ ml mgl kl l c ll 2 2 22 2 2 sin sin cos ˙ cos θθθ =− When θ is small, sin θ θ and cos θ 1 ml cl kl mgl ml cl kl mg 2 42 0 0 ˙ ˙ θθ ++− = = For stability, kl mg 2 > and c > 0. The result of adding a dashpot is asymptotic stability.

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1.81 Replace the massless rod of the inverted pendulum of Figure 1.36 with a solid object compound pendulum of Figure 1.19(b). Calculate the equations of vibration and discuss values of the parameter for which the system is stable.
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## This note was uploaded on 02/11/2010 for the course MECHANICAL ms316 taught by Professor Abduljaba during the Spring '09 term at Kalamazoo.

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SolSec1.8 - Problems and Solutions Section 1.8 (1.80...

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