A heavy table is supported by flat steel legs Its natural pe

A heavy table is supported by flat steel legs. Its natural period in horizontal motion is 0.4 s. When a 30 kg plate is clamped to its surface, the natural period in horizontal motion is increased to 0.5 s. What is the effective spring constant and the mass of the table ?

Solution

Time period T = 2*pi*sqrt(m/k)

0.4 = 2*3.14*sqrt(m/k)

0.5 = 2*3.14*sqrt((m+30)/k)

Dividing both equations, 0.5/ 0.4 = sqrt [(m+30)/m]

Table mass m = 53.33 kg

0.4 = 2*3.14*sqrt(53.33/k)

Stiffness k = 13159.5 N/m