There is a following water tank structure which has a capaci

There is a following water tank structure which has a capacity of 20 x 103kg. In the cases of empty and full, each transverse vibrational period is 1.0 sec and 2.5 sec, respectively. Compute the weight (W) and transverse stiffness (k). lu u(t) ??

Solution

Solution:-

Given

Empty weight of tank = W

Mass of filled water tank = W/g + 20 *10³

Transverse stiffness = k

Vibration time period(T₁) = 1 second   (for empty tank)

T₂ = 2.5 second          (for filled tank)

We know that

T₁ = 2(pi)*sqrt(M/k)

1 = 2(pi) * sqrt((W/g)/k)

Squaring both side

k = 4(pi)² * W/g          - - - - - (1)

For

T₂ = 2(pi) *sqrt((W/g + 20*10³)/k)

2.5 = 2(pi) *sqrt((W/g + 20*10³)/k)

On squaring both side

6.25 = 4(pi)² * (W/g + 20 *10³)/k

k = 4(pi)² *(W/g + 20 *10³)/(6.25)        - - - - - -(2)

On equating equation (1) and (2)

4(pi)² *W/g = 4(pi)² * (W/g + 20 *10³)/(6.25)

6.25 *W/g = W/g + 20*10³

5.25 *W/g = 20*10³

W = 20 *10³ *9.8/(5.25)

W = 37333.33 N Answer

On putting value of W = 37333.33 in equation (1)

k = 4(pi)² * 37333.33/9.8

k = 150.39 * 10³ N/m      Answer