Simple horizontal mass

Question

what is the maximum kenetic energy of a simple horizontal mass-spring oscillator whose eqaution of motion is given by x = (3.50 m)(sin(7t)? the mass of the end of the string is 900 g

Answer 1

maximum kinetic energy occurs when the potential energy is at a minimum, or the displacement of the spring is zero. Thus KE = 1/2 m V^2 = 1/2 k x^2. In this case you need to take derivatives to find the max KE.