Problem 9: A spring whose spring constant is 80.0 N/m vertically supports a mass of 1.0 kg is at the rest position. Find the distance by which the mass must be pulled down, so that on being released, it may pass the mean position with maximum velocity of one meter per second?

Solution

Given data             spring constant = 80 N/m                     Mass attached = 1 kg

                               Maximum velocity = 1 m/s                 

Required                 Maximum distance from the mean position =?

Formula

Here v₀ is the maximum velocity and x₀ is the maximum distance from the mean position. Put the values,