Block A of mass 40 kg is suspended from the ceiling by a spr

Block A of mass 40 kg is suspended from the ceiling by a spring with stiffness constant k1 = 900 N/m, and a dashpot (damper) of strength C. The mass moves only in the vertical direction, without rotation.

Part A. Find the period of natural vibration of A. Assume that C = 0.

Part B. Suppose that A is vibrating in the vertical direction, with an amplitude of vibration equal to 5 mm (10 mm peak to peak). Find the maximum acceleration of A. Assume that C = 0.

Part C. Find the value of C that would be required to reduce the amplitude of vibration of A from 0.5 meters to 0.2 meters, in 15 seconds?

Part D. Suppose that an earthquake were to make the ceiling vibrate vertically with an amplitude of 3 mm, at a frequency of 5 radians/second. Find the amplitude of vibration of A. Assume C = 0.

Solution

Block A of mass 40 kg is suspended from the ceiling by a spring with stiffness constant k1 = 900 N/m, and a dashpot (damper) of strength C. The mass moves only in the vertical direction, without rotation.

Part A. Find the period of natural vibration of A. Assume that C = 0.

Part B. Suppose that A is vibrating in the vertical direction, with an amplitude of vibration equal to 5 mm (10 mm peak to peak). Find the maximum acceleration of A. Assume that C = 0.

Part C. Find the value of C that would be required to reduce the amplitude of vibration of A from 0.5 meters to 0.2 meters, in 15 seconds?

Part D. Suppose that an earthquake were to make the ceiling vibrate vertically with an amplitude of 3 mm, at a frequency of 5 radians/second. Find the amplitude of vibration of A. Assume C = 0.