Question

$\text{A 3 kg mass is suspended in a box by aspring as shown in figure. The box put on a plate form having vibration}y=0.8\sin 6t\text{cm. The absolute amplitude of the mass given}k=6000\text{N/m is}$

• A. 0.0146 cm
• B. 0.8 cm
• C. 0.814 cm
• D. 0.9 cm

Answer 1

The correct option is C 0.814 cm

$\frac{x}{y}=\frac{r^2}{1-r^2}$

$y=Y\sin 6t\text{cm}$

$Y=0.8\text{cm,}\omega =6\text{rad/s}$

$r=\frac{\omega }{{\omega }_n}$

${\omega }_n=\sqrt{\frac{k}{m}}=\sqrt{\frac{6000}{3}}=44.72\text{rad/s}$

$r=\sqrt{\frac{\omega }{{\omega }_n}}=\frac{6}{44.72}=0.134$

$r^2=0.018$

$\frac{x}{0.8}=\frac{0.018}{1-0.018}$

$\Rightarrow x=0.0146\text{cm}$

Thus the absolute amplitude of mass,
$A=x+y=0.0146+0.8=0.814\text{cm}$