The rodd surface varies sinusoidally with an amp of 0.05 m and a wave length of 6 m.

Given:

M = 1200 kg

K = 400 KN/m = $400 \times 10^3$ N/m

$\xi$ = 0.5

V = 20 km/hr = $\frac{20 \times 10^3}{3600} = 5.55$ m/s

Y = 0.05m

$\lambda$ = 6m

Amp ratio is given by,

$\frac{x}{y} = \frac{\sqrt{1 + (2 \xi r)^2}}{\sqrt{ (1-r^2)^2 + (2 \xi r)^2}}$

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

$Wn = \sqrt{k/m} = \sqrt{ \frac{400 \times 10^3}{1200}} = 18.25$ rad/s

$w = 2 \pi f$

$f = \frac{v}{x} = \frac{(20 \times 1000/3600)}{6} = 0.925$ Hz

$w = 2 \pi \times 0.925 = 5.82$ rad/sec

$r = \frac{5.82}{18.25} = 0.31878$

$\frac{x}{0.05} = \frac{1.049}{0.9532}$

X = 0.0550 m