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?
A block of mass 200 g is attached at the end of a massless spring of spring constant 100 N/cm. The other end of the spring is attached to the ceiling and the mass is brought to rest at a point . Point is taken to be the zero of the potential energy of the block, both from the weight and the spring force. The mass hangs freely and the spring is in a stretched state. The block is then pulled downward by another 5.00 cm and released from rest.
What is the net potential energy of the block at the instant the block is at the lowest point?
What is the net potential energy of the block at the instant the block returns to the point marked ?
What is the speed of the block as it crosses the point marked ?
How high above the point marked does the block rise before coming to rest again?
Consider a 0.750-kg object on a horizontal surface connected to a spring that has a force constant of 150 N/m. There is simple friction between the object and surface with a static coefficient of friction .
How far can the spring be stretched without moving the mass?
The mass is set into oscillations that have an amplitude equal to twice the maximum distance that the spring can stretch without moving the object. During these oscillations, the kinetic coefficient of friction . If the object starts oscillating with maximum initial displacement, what total distance will it move before it comes to rest?