Question

current attempt in progress
the kinetic energy of an object attached to a horizontal ideal spring is denoted by ke and the elastic potential energy by pe. for the simple harmonic motion of this object the maximum kinetic energy and the maximum elastic potential energy during an oscillation cycle are ( ke_{max} ) and ( pe_{max} ), respectively. in the absence of friction, air resistance, and any other nonconservative forces, which of the following equations applies to the object - spring system?
a. ( ke + pe = \text{constant} )
b. ( ke_{max} = pe_{max} )
neither a, nor b
a and b
b, but not a
a, but not b

Explanation:

According to the law of conservation of mechanical energy, in the absence of non - conservative forces (such as friction, air resistance), the total mechanical energy of the object - spring system is conserved. The total mechanical energy \(E = KE+PE\). At the equilibrium position, the elastic potential energy \(PE = 0\) and \(KE = KE_{max}\). At the maximum displacement (amplitude) position, the kinetic energy \(KE = 0\) and \(PE=PE_{max}\). Since \(E = KE + PE\) is constant, when \(KE = KE_{max}\), \(PE = 0\) and when \(PE = PE_{max}\), \(KE = 0\). So \(KE_{max}=PE_{max}\) (because \(E = KE_{max}+0=0 + PE_{max}\)). Also, \(KE + PE=E\) (constant) at any point in the motion.

Answer:

A and B