00:01
Hello students, in the question here first of all talking about the resonant frequency, the resonant frequency can be calculated using the formula f equals to 1 upon 2 pi under root k upon m where f is the resonant frequency, k is the spring constant and m is the mass of the system.
00:28
Here putting in the values we have the value of k equals to 4 by 3 into 45000 into pi into 2 .5 upon 2 whole cube, we get k equals to 22 double 1 9 8 newton per meter.
00:53
Also the mass is equals to 27508 kg.
00:59
Substituting values in resonant frequency we get resonant frequency f equals to 1 upon 2 pi under root k that is 2 2 1 1 9 8 upon m that is 27508.
01:17
Solving we get the resonant frequency f equals to 3 .05 hertz.
01:23
Now the amplitude of vertical and the sliding vibration at resonant frequency can be calculated using the formula a equals to q o upon m omega square under root 1 minus omega square upon omega n square.
01:46
Again putting in the values and solving for a we have the value of a equals to 27 upon 10 to the into 10 to the power 3 upon 27508 into 19 .17 square under root 19 .17 square upon 19 .17 square.
02:29
Solving for the value of a we get a equals to 0 .001 meter.
02:37
Next calculating the amplitude for sliding the a sliding is equals to a vertical into poisson's ratio...