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108. Problem 15.23 (RHK) Three 10,000 kg ore-cars are held at rest on a 26.00 incline on a mine railway using a cable that is parallel to the incline. The cable is observed to stretch 14.2 cm just before coupling breaks, detaching one of the cars. We have to find (a) the frequency of the resulting oscillations of the remaining two cars and (b) the amplitude of the oscillations.
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Solution: Click For PDF Version Mass of each car is 10,000 kg. Cable is stretched by 14.2 cm just before the cable breaks. We can determine the force constant of the cable using this information.
Equation of motion of the remaining two cars after one of the cars gets detached from the cable is
Let us call
Equation of motion can be expressed as
It is an equation of SHM. As the SHM of the remaining two cars will be
centred around
Frequency of SHM will be
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, and the
third car gets detached from the cable when it is stretched by 14.2 cm, the
amplitude of oscillations will be
