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 = constant
b. ke_max = pe_max
○ b, but not a
○ a, but not b
○ a and b
○ neither a nor b

Explanation:

• For option A: In the absence of non - conservative forces (friction, air resistance etc.), the total mechanical energy of the object - spring system is conserved. The total mechanical energy \(E = KE+PE\). So \(KE + PE=\text{constant}\).
• For option B: 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 the total mechanical energy \(E=KE + PE\) is constant, \(E=KE_{max}+0=0 + PE_{max}\). So \(KE_{max}=PE_{max}\)

Answer:

C. A and B