A senstive computer is being transported in a boxcar. Accelerometer measurements tell us that at its normal speed, the foremost component of the boxcar's vertical acceleration is 10 m/s^2 at a frequency of 30 rad/sec. The crate in which the vase is being transported is tied to the floor of the boxcar. What is the required frequency ratio of an isolator with a damping ratio of 0.1 such that the acceleration amplitude of the 15 kg vase is less than 0.5 m/s^2

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initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft