A 0.750 kg mass hangs from a vertical spring. Assume the mass of the spring is negligible. Note that the force due to the initial stretching of the spring essentially cancels out the contribution of the gravitational force. The potential energy of the system can be written as U = (1/2)ky^2, where y is measured from the equilibrium position and there is no gravitational term (because it was canceled out). Thus the vertical spring behaves just like a horizontal spring. When you hang the mass on the spring, the equilibrium position is 0.350 m below the un-stretched position of the spring. What is the value of the force constant of the spring? (Hint: Use the force required to stretch the spring.) Find the frequency and period of this system. You pull the spring down 0.150 m below the equilibrium position and release it from rest. Write an equation for the position of the mass as a function of time y(t).
A 0.750 kg mass hangs from a vertical spring. Assume the mass of the spring is negligible. Note that the force due to the initial stretching of the spring essentially cancels out the contribution of the gravitational force. The potential energy of the system can be written as U = (1/2)ky^2, where y is measured from the equilibrium position and there is no gravitational term (because it was canceled out). Thus the vertical spring behaves just like a horizontal spring.
When you hang the mass on the spring, the equilibrium position is 0.350 m below the un-stretched position of the spring. What is the value of the force constant of the spring? (Hint: Use the force required to stretch the spring.)
Find the frequency and period of this system.
You pull the spring down 0.150 m below the equilibrium position and release it from rest. Write an equation for the position of the mass as a function of time y(t). Let t = 0 represent the time when you release the mass. Use the equation to find the positions of the mass at t = 0.250 s and t = 2.25 s.
What is the velocity of the mass at the equilibrium position, y = 0? At y = 0.0500 m? At y = 0.150 m?
Find the length of a simple pendulum with the same period as the mass on the spring system above.
Find the length of a physical pendulum made of a solid rod that pivots about an axis on one end and has the same period as the mass on the spring system above.
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