In simple harmonic motion (SHM), when the displacement is one-half the amplitude (A), the kinetic energy (KE) and potential energy (PE) can be calculated using the formulas KE = (1/2)mv^2 and PE = (1/2)kx^2. At this displacement, the fraction of total energy that is kinetic energy is 3/4, while potential energy constitutes 1/4 of the total energy. This conclusion is derived from the relationship between kinetic and potential energy in SHM, where total energy remains constant.
PREREQUISITESStudents studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators seeking to clarify concepts of energy in simple harmonic motion.
armolinasf said:Homework Statement
(a) When the displacement in SHM is one-half the amplitude A, what fraction of the total energy is kinetic energy? What fraction is potential?
The Attempt at a Solution
I tried finding a ratio of KE/t, where t=KE+PE and PE/t but I got answers that didn't quite make sense how am I going about this the right way? As always thanks for the help