00:01
Hello students, in this question first we need to find frequency of undamped vibration.
00:07
For that let us find stiffness.
00:10
As there are three springs, the total stiffness will be 3 into stiffness of each spring that is given in the question 9 kilo newton.
00:20
From this, the total stiffness will be 27 kilo newton per meter.
00:27
Natural frequency is given by root of stiffness divided by mass that is stiffness 27 into 10 power 3 divided by 70.
00:37
This gives us 19 .6 which is approximately equal to 20 radian per second.
00:44
To find frequency of undamped vibration, we know that omega n by 2 pi which is equal to 20 divided by 2 into 3 .142 which gives the frequency of undamped vibration as 3 .125 hertz.
01:10
Next we need to calculate frequency of damped vibration.
01:15
Frequency of damped vibration is given by omega d by 2 pi which can be found by using omega n whole square minus constant a square divided by 2 pi.
01:32
Here first we need to find the value of a.
01:35
For that let us consider amplitude of first vibration x1 and amplitude after one complete oscillation x3 is the amplitude after two complete oscillation.
01:51
We know that ratio of first two amplitude is equal to ratio of next two amplitude...