Question

Suppose that you are designing a new shock absorber for an automobile. The car has a mass of 1000 kg (kilograms) and the combined effect of the springs in the suspension system is that of a spring constant of 4000 N/m (i.e.each of the four springs has a spring constant of 1000 N/m). Before a damping mechanism is installed in the car, when the car hits a bump it will bounce up and down. How may bounces will a rider experience in the minute right after the car hits a bump? Alternatively, what is the frequency in cycles per minute?

Answer 1

Answer:

4.77, approximately 5 cycles per minute

Step-by-step explanation:

For a loaded spring, the frequency of oscillation is given by

$f=\dfrac{1}{2\pi}\sqrt{\dfrac{m}{k}}$

where $m$Vis the mass of the load and $k$ is spring constant.

Substituting values in the question,

$f=\dfrac{1}{2\pi}\sqrt{\dfrac{1000}{4000}}$

$f=\dfrac{1}{2\pi}\sqrt{\dfrac{1}{4}}$

$f=\dfrac{1}{2\pi}\times\dfrac{1}{2}$

$f=\dfrac{1}{4\pi}$

This value is in units of oscillations per second. To convert to oscillations per minute, we divide by $\frac{1}{60}$ or, in essence, multiply $f$ by 60.

Thus, we have

$f=\dfrac{1}{4\pi}\times60$

$f=\dfrac{15}{\pi}= 4.77 \text{ cycles per minute}$