Question

(a) When the displacement in SHM is one-sixth the amplitude xm, what fraction of the total energy is kinetic energy? (b) What fraction is potential energy? (c) At what displacement, in terms of the amplitude, is the energy of the system half kinetic energy and half potential energy? (Use any variable or symbol stated above as necessary.)

Answer 1

Step-by-step explanation:

`KE = (1)/(2)* K* (A^2-X^2)`

at
`X = (1)/(6)A\\\\ KE = (1)/(2)* K* ( A^2 - A^{(2)/(36))\\\\ fraction = (35)/(36) = 0.9722`

b) PE fraction = 1/36 = 0.02777

c) 1/2*KX^2 = 1/2*K*(A^2-X^2)

=> X = A/sqrt(2)