Suppose a 32-pound weight stretches a spring 2 feet. If the weight is released from rest at the equilibrium position, find the equation of motion x(t) if an impressed force f(t) = 12t acts on the system for 0 ≤ t < 5 and is then removed (see Example 5 in Section 7.3). Ignore any damping forces. (Use g = 32 ft/s2 for the acceleration due to gravity.)

Acylinder with a movable piston contains 11.7 moles of a monatomic ideal gas at a pressure of 1.32×10^5 pa. the gas is initially at a temperature of 300 k. an electric heater adds 43200 j of energy into the gas while the piston moves in such a way that the pressure remains constant. cp=20.79 j k^−1 mol^−1 for a monatomic ideal gas, and that the number of gas molecules is equal to avogadro's number (6.022×10^23) times the number of moles of the gas. (a) what is the temperature of the gas after the energy is added? (b) what is the change in volume of the gas? (c) how much work is done by the gas during this process?