Question

A 2.0-kg cart attached to a spring undergoes simple harmonic motion so that its displacement is described by x=(0.20m)sin[(2π/2.0s)t].

Answer 1

Answer:THe total energy can be found from the maximum kinetic energy since energy is conserved.  Kinetic energy is

K = 1/2 mv^2  and v = dx(t)/dt = (0.2)(2*pi/2)cos((2*pi/2)t)

vmax = 0.2*pi m/s  when t = 0 so  the total energy is  

E = 1/2 mvmax^2 = 1/2 m*0.04*pi^2 = 0.1257 J

Step-by-step explanation: