The amplitude of a simple harmonic oscillator has decreased from 40cm to 38cm. What percentage of energy did the harmonic oscillator lose?

It is recommended to start off by converting all given data into SI units to avoid confusion later on. Write down the total energy of the system and that it is conserved: E(tot)= KE+PE and KE=(mv^2)/2; PE=(kx^2)/2. The potential energy is directly proportional to the amplitude, thus it is easy to estimate the change. As for the kinetic energy, the speed is equal to v=wx and thus, the kinetic energy is KE=(mw^2x^2)/2. Find the relationships between kinectic/potential energies of 40 cm and 38cm amplitudes. For an example: PE1/PE2=(kx1^2)/2 * 2/(kx2^2) = x1^2/x2^2 = 1.108. Later it is found that KE1/KE2=PE1/PE2=1.108. Now with all the components gathered it is possible to find the change in total energy of the system: E2(tot)/ E1(tot) = (KE2+PE2) / (KE1+PE1) = (KE2+PE2)/( 1.108(KE2+PE2)) = 0.9100%=90%. The loss of energy is 100%-90%=10%.