An 85.0-kg man climbs onto a 900-kg car with worn out shock absorbers and whose springs have an effective force constant of 125 kN/m. As he drives along, he hits a bump, and this starts the car oscillating with simple harmonic motion. What is the smallest amplitude of the oscillations that will cause him to bounce from his seat?

Question

Quizplus · Accepted Answer

The smallest amplitude that will cause the man to bounce from his seat is when the acceleration of the car equals the acceleration due to gravity. Using the formula for maximum acceleration in simple harmonic motion, $ a_{max} = \omega^2 A $, where $ \omega = \sqrt{\frac{k}{m}} $, and setting $ a_{max} = g $, we solve for $ A $. With $ k = 125,000 \, \text{N/m} $ and $ m = 985 \, \text{kg} $, we find $ A \approx 7.73 \, \text{cm} $.

An 850-Kg Man Climbs onto a 900-Kg Car with Worn Out