You are riding in an automobile of mass $3000 \mathrm{~kg}$. Assuming that you are examining the oscillation characteristics of its suspension system. The suspension sags $15 \mathrm{~cm}$ when the entire automobile is placed on it. Also, the amplitude of oscillation decreases by $50 \%$ during one complete oscillation. Estimate the values of (a) the spring constant $\mathbf{k}$ and (b) the damping constant b for the spring and shock absorber system of one wheel, assuming that each wheel supports $750 \mathrm{~kg}$.

Home » You are riding in an automobile of mass . Assuming that you are examining the oscillation characteristics of its suspension system. The suspension sags when the entire automobile is placed on it. Also, the amplitude of oscillation decreases by during one complete oscillation. Estimate the values of (a) the spring constant and (b) the damping constant b for the spring and shock absorber system of one wheel, assuming that each wheel supports .

You are riding in an automobile of mass $3000 \mathrm{~kg}$ . Assuming that you are examining the oscillation characteristics of its suspension system. The suspension sags $15 \mathrm{~cm}$ when the entire automobile is placed on it. Also, the amplitude of oscillation decreases by $50 \%$ during one complete oscillation. Estimate the values of (a) the spring constant $\mathbf{k}$ and (b) the damping constant b for the spring and shock absorber system of one wheel, assuming that each wheel supports $750 \mathrm{~kg}$ .

You are riding in an automobile of mass $3000 \mathrm{~kg}$ . Assuming that you are examining the oscillation characteristics of its suspension system. The suspension sags $15 \mathrm{~cm}$ when the entire automobile is placed on it. Also, the amplitude of oscillation decreases by $50 \%$ during one complete oscillation. Estimate the values of (a) the spring constant $\mathbf{k}$ and (b) the damping constant b for the spring and shock absorber system of one wheel, assuming that each wheel supports $750 \mathrm{~kg}$ .

(a) Mass of the automobile is given as $=3000 \mathrm{~kg}$

The suspension sags by a length of $15 \mathrm{~cm}$

Decrease in amplitude $=50 \%$ during one complete oscillation

If each spring’s spring constant is $k$ , the spring constant of the four springs in parallel equals

$\mathrm{K}=4 \mathrm{k}$

Since $F=4 k x$

$\mathrm{Mg}=4 \mathrm{kx}$

$\Rightarrow k=M g / 4 x=(3000 \times 10) /(4 \times 0.15)=5 \times 10^{4} \mathrm{~N}$

(b) Each wheel supports $750 \mathrm{~kg}$ weight

$\mathrm{t}=2 \pi \sqrt{\mathrm{m}} / \sqrt{\mathrm{k}}=2 \times 3.14 \times\left(\sqrt{\left.750 / \sqrt{5} \times 10^{4}\right)}=0.77 \mathrm{sec}\right.$