A mass attached to a spring has 4 J of potential energy when stretched to its full amplitude. The kinetic energy of the mass halfway to equilibrium is

A linear spring is compressed by 0.135 m from its equilibrium position. If it stores 6.1 J of energy in this state, what is its spring constant?

hass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from a point 9 inches below the equilibrium position. (a) Find the position x of the mass at the timest= 1/12, 1/8, 1/6, 11/4, and 91/32 s. (Use g = 32 ft/s? for the acceleration due to gravity.) x(n/12) = ft x(n/8) = ft x(п/6) — ft x(п/4) — ft x(9n/32) ft (b) What is the velocity of the mass when t = 3t/16 s? ft/s In which direction is the mass heading at this instant? O downward O upward (c) At what times does the mass pass through the equilibrium position? п 3D 0, 1, 2, ..

A mass of 0.69 kg is is initially traveling at 6.19 m/s across a horizontal, frictionless surface. It then reaches a spring with a fixed end having a spring constant of 334 N/m that is positioned horizontally and initially at equilibrium. The incoming mass will then contact the spring, compressing it as it comes to rest. What is the speed of the mass upon the spring being compressed by 0.173 m from its equilibrium position?

Using the spring force, F = -kx, calculate: a) The work done by an external force stretching the spring a distance L away from the equilibrium length. b) At a stretch length L, how much potential energy is stored in the spring? If a mass m is attached to the spring and released from a stretch length L, what is the maximum velocity c) of the mass? d) At what x coordinate does this maximum velocity occur?

A 7.0 kg block on a horizontal, frictionless surface is attached to a light spring (force constant = 1.2 kN/m). The block is initially at rest at its equilibrium position when a force of magnitude P acting parallel to the surface is applied to the block, as shown. When the block is 8.0 cm from the equilibrium position, it has a speed of 0.80 m/s. How much work is done on the block by the force P as the block moves the 8.0 cm? A. 7.4 J B. 5.4J C. 6.1J D. 6.7J E. 4.9J

Please answer questions 3, 4 and 5! A 780 g object is hung from a spring with a force constant of 30 N/m. What is the displacement of the spring from equilibrium length if it is hanging vertically Now, the mass in question a is being pulled downward by an additional 9 cm. What is the potential energy? You release the object, what is the period of oscillation of the mass/spring system?  Using yt=Acos(wt), what is the expression of the vertical motion along the y-axis?  What is the maximum speed of the oscillating object? What is the maximum kinetic energy? Do these values make sense from the values in part b?