Question

Which of the following statements is not true regarding a mass–spring system that moves with simple harmonic motion in the absence of friction? (a) The total energy of the system remains constant. (b) The energy of the system is continually transformed between kinetic and potential energy. (c) The total energy of the system is proportional to the square of the amplitude. (d) The potential energy stored in the system is greatest when the mass passes through the equilibrium position. (e) The velocity of the oscillating mass has its maximum value when the mass passes through the equilibrium position.

Short answer

Statement (d) wrong, because the elastic potential energy of the system is minimum and the kinetic energy is a maximum

Step-by-step solution

Step 1: The elastic potential energy of the system

$P{E}_s=\frac{1}{2}k{x}^2$

$P{E}_s=$Elastic potential energy

$k=$Elastic constant

$m=$Displacement

Find which statement is not true

Answer (d) is the only false statement. At the equilibrium position, x= 0, the elastic potential energy of the system $P{E}_s=\frac{1}{2}k{x}^2$is a minimum and the kinetic energy is a maximum.