Find stiffness K if only 10% of the shaking force is to be transmitted to the supporting structure neglected damping.

m = 30 kg

No of springs = S

N = 580 rpm

$w = \frac{2 \pi \times 580}{60} = 60.73$ r/sec

$T_r$ = 0.10

$0.10 = \frac{1}{r^2 - 1}$

$0.10 (r^2 – 1) = 1$

$r^2 = 11$

R = 3.36

$r = \frac{w}{w_n}$

$3.36 \times w_n = 60.73$

$W_n = 18.31 \ r/sec$

$w_n = \sqrt{ \frac{3k}{m}}$

$(18.31)^2 = \frac{ 3 \times k}{30}$

$ k = 3.35 \times 10^3$ N/m