Unit 5 - Problem 3 ==> Shock Absorber Period

Given:

• $$ \mbox{mass of the car} = 2,000  \mbox{kilograms} $$
• $$ \mbox{four shock absorbers with four wheels}$$
• $$ \mbox{each shock absorber has }  k = 100,000 $$
• $$ \mbox{gravity}  = 10 $$ 

Rationale:

• $$ T_{period-shock-absorber} = 2 \pi \sqrt\frac{m_{on-shock-absorber}}{k} $$
• $$ m_{on-shock-absorber} = \frac{m_{car}}{4} $$
• $$ T_{period-shock-absorber} = 2 \pi \sqrt\frac{\frac{m_{car}}{4}}{k} = 2 \pi \sqrt\frac{m_{car}}{4 k} $$

Calculate:

• $$ T_{period-shock-absorber} = 2 \pi \sqrt\frac{2,000}{4 * 100,000} $$
• $$ T_{period-shock-absorber} = \frac{44}{7} \sqrt{.005} = 6.2857 * .07071 = 0.44 $$