Question

Inside a NASA test vehicle, a 3.50kg ball is pulled along by a horizontal ideal spring fixed to a friction-free table. The force constant of the spring is 229 N/m. The vehicle has a steady acceleration of 5.00m/s^2, and the ball is not oscillating. Suddenly, when the vehicle's speed has reached 45.0m/s, its engines turn off, thus eliminating its acceleration but not its velocity. What is the frequency? ...?

Answer 1

F = mx'' = -kx => x'' + (k/m)x = 0 => x(t) has period T T = 2π / sqrt k/m
f = 1/T= sqrt k/m/2π
f = sqrt k/m/2π = sqrt 229/3.5 /2π = 1.29 sec − 1

This is the frequency of a vehicle that has a steady acceleration of 5.00m/s^2, and when the vehicle's speed has reached 45.0m/s, its engines turn off, thus eliminating its acceleration but not its velocity.

Thank you for posting your question. I hope that this answer helped you. Let me know if you need more help.