Final answer:
In SHM, when the displacement is 0.84 times the maximum displacement, the fraction of the total energy that is kinetic energy is 29.44%.
Step-by-step explanation:
When the displacement in Simple Harmonic Motion (SHM) is x = 0.84 xm, we can determine the fraction of the total energy that is kinetic energy. In SHM, the total energy (Etotal) is conserved and is the sum of potential energy (U) and kinetic energy (K). According to the energy conservation in SHM, Etotal = U + K = constant.
The potential energy in SHM is given by U = (1/2)kx2, where k is the spring constant and x is the displacement. The kinetic energy can be found by subtracting the potential energy from the total energy, K = Etotal - U. At maximum displacement xm, the potential energy is maximum and kinetic energy is zero, therefore Etotal = Umax = (1/2)kxm2.
When the displacement is x = 0.84 xm, the potential energy is U = (1/2)k(0.84 xm)2 = (1/2)k(0.7056 xm2). The kinetic energy at this point is K = (1/2)kxm2 - (1/2)k(0.7056 xm2) = (1/2)kxm2(1 - 0.7056) = (1/2)kxm2 * 0.2944.
Therefore, the fraction of the total energy that is kinetic energy when the displacement is x = 0.84 xm is 0.2944 or 29.44%.