Consider a large crane holding a car of mass M = 1100 kg as shown in the figure.

Question

Consider a large crane holding a car of mass M = 1100 kg as shown in the figure. The cable is L = 7.9 m long and has a density of = 1.9 kg/m. It is a very breezy day and the cable starts to vibrate in the wind.

Part (a) Give an expression for the fundamental frequency of the cable's vibration.

Part (b) What would this frequency be in Hz?

Part (c) What would the mass of the car, M2, have to be so that the second harmonic vibration of the cable was the same frequency as the fundamental from part (b)?

Explanation / Answer

a) f = 1/2L)*sqrt(T/u) = (1/2L)*sqrt(Mg/u)

b) f = (1/15.8)*sqrt((1100*9.8)/(1.9)) = 4.767 Hz
===========================

c) f2 = 2f = (1/2L)*sqrt((M2*g)/u)

9.535 = (1/15.8)*sqrt((m2*9.8)/(1.9))

M2 = 4400.245 kg

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.