A mass is attached to a spring and hung vertically. The mass is raised a short distance in the vertical direction and released. The mass oscillates with a frequency . If the mass is replaced with a mass nine times as large, and the experiment was repeated, what would be the frequency of the oscillations in terms of ?
Near the top of the Citigroup Center building in New York City, there is an object with mass of kg on springs that have adjustable force constants. Its function is to dampen wind-driven oscillations of the building by oscillating at the same frequency as the building is being driven—the driving force is transferred to the object, which oscillates instead of the entire building.
What effective force constant should the springs have to make the object oscillate with a period of 2.00 s?
What energy is stored in the springs for a 2.00-m displacement from equilibrium?
A block with a mass of 2.0 kg lies at rest on a frictionless table. A spring, with a spring constant of N/m is attached to a wall at one end of the table, and the other end of the spring is attached to the block. A second block, of mass 0.50 kg, is placed on top of the first block, the centers of the blocks aligned with each other. The 2.0-kg-mass block is gently pulled away from the wall, to a position , and released from rest, after which the blocks oscillate on the end of the spring. There is a coefficient of friction of 0.45 between the two blocks as they oscillate.
What is the period of the oscillations of the system of blocks?
What is the largest value of initial spring extension for which the centers of the two boxes remain aligned at all times during the boxes oscillation?