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

sqrt(k/m)/2pi is getting me 12.7 but it says thats wrong

Answer 2

F = mx'' = -kx
=> x'' + (k/m)x = 0
=> x(t) has period T
\[ T = 2\pi / \sqrt{k/m} \ \implies f = \frac{1}{T} = \sqrt{k/m}/2\pi \]
hence
\[ f = \sqrt{k/m}/2\pi = \sqrt{229/3.5}/2\pi = 1.29 \ sec^{-1} \]