Question

Problem 2: (a) In this exercise a massless spring with a spring constant k = 6 N/m is stretched from its equilibrium position with a mass m attached on the end. The distance the spring is stretched is x = 0.3 m. What is the force exerted by the spring on the mass? (5 points)

(b) If we were to stretch the spring-mass system as in part (a) and hold it there, there will be some initial potential energy associated with the spring-mass system. Then when we release the system, the initial potential energy will get converted into kinetic energy. The kinetic energy will increase as the mass accelerates toward its equilibrium position at which it will overshoot, and the spring will begin to compress and retard the motion of the mass. Kinetic energy after it passes the equilibrium position will begin to decrease and eventually will all get converted back into potential energy once the spring is fully compressed the same distance away from its equilibrium position. If no dissipative forces are present, then the energy is conserved throughout the entire motion and the mass will oscillate back and forth. (b) Using conservation of energy and the values from part (a) (k and x) and given the mass at the end of the spring is m = 6 kg, calculate the linear speed of the mass m when it is instantaneously at its equilibrium position during its motion as described above. (10 points)

Answer 1