Question

Problem 21.44 The 4-kg slender bar is 2 m in length. Aerodynamic drag on the bar and friction at the sup- port exert a resisting moment about the pin support of magnitude 1.4(d?/dt) N-m, where d?/dt is the angular velocity in rad/s. (a) What are the period and frequency of small vibra- tions of the bar? (b) How long does it take for the amplitude of vibration to decrease to one-half of its initial value? Solution: (a) ? M0 = I0?: -1.4 d?/dt - mg (L/2) sin ? = 1/3 mL^2 ?. The (linearized) equation of motion is d^2?/dt^2 + (4.2/mL^2) d?/dt + (3g/2L) ? = 0. This is of the form of Eq. (21.16) with d = 4.2/mL^2 = 4.2/(4)(2)^2 = 0.2625 rad/s.

          Problem 21.44 The 4-kg slender bar is 2 m in length.
Aerodynamic drag on the bar and friction at the sup-
port exert a resisting moment about the pin support of
magnitude 1.4(d?/dt) N-m, where d?/dt is the angular
velocity in rad/s.

(a) What are the period and frequency of small vibra-
tions of the bar?
(b) How long does it take for the amplitude of vibration
to decrease to one-half of its initial value?

Solution:

(a) ? M0 = I0?:

-1.4 d?/dt - mg (L/2) sin ? = 1/3 mL^2 ?.

The (linearized) equation of motion is

d^2?/dt^2 + (4.2/mL^2) d?/dt + (3g/2L) ? = 0.

This is of the form of Eq. (21.16) with

d = 4.2/mL^2 = 4.2/(4)(2)^2 = 0.2625 rad/s.

Problem 21.44 The 4-kg slender bar is 2 m in length.
Aerodynamic drag on the bar and friction at the sup-
port exert a resisting moment about the pin support of
magnitude 1.4(d?/dt) N-m, where d?/dt is the angular
velocity in rad/s.

(a) What are the period and frequency of small vibra-
tions of the bar?
(b) How long does it take for the amplitude of vibration
to decrease to one-half of its initial value?

Solution:

(a) ? M0 = I0?:

-1.4 d?/dt - mg (L/2) sin ? = 1/3 mL^2 ?.

The (linearized) equation of motion is

d^2?/dt^2 + (4.2/mL^2) d?/dt + (3g/2L) ? = 0.

This is of the form of Eq. (21.16) with

d = 4.2/mL^2 = 4.2/(4)(2)^2 = 0.2625 rad/s.

Added by Carolina S.

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