The potential energy of an SHM oscillator is given by U = 0.5kx² and kinetic energy by K = 0.5k(A²-x²). Setting U = K leads to x² = A²/2, or x = ±A/√2. The provided answer '0' is physically incorrect as potential energy is zero at equilibrium (x=0) while kinetic energy is maximum. The answer key is preserved as requested.

At the mean position of SHM, the displacement is zero. Since potential energy (1/2kx^2), restoring force (-kx), and acceleration (-ω^2x) are all functions of displacement, they all become zero at the mean position. Simultaneously, the velocity is at its maximum, resulting in maximum kinetic energy. Therefore, all listed quantities are zero.

In simple harmonic motion, the potential energy of a spring-mass system is given by U = 0.5kx². At the extreme positions (maximum displacement), the displacement x is at its maximum, resulting in the maximum potential energy. At the equilibrium position, the potential energy is zero.

In simple harmonic motion, the velocity of the mass is at its peak as it passes through the equilibrium (mean) position. Since kinetic energy is proportional to the square of velocity (KE = 1/2mv^2), the kinetic energy reaches its maximum value at this point, while potential energy is at its minimum.

At the extreme position (amplitude) of simple harmonic motion, the velocity of the oscillating mass is momentarily zero. Since kinetic energy is defined as 1/2mv^2, the kinetic energy at this point is zero, with all energy stored as potential energy.

In an ideal simple harmonic motion (SHM) system without friction or damping, the total mechanical energy is the sum of kinetic and potential energy. This total energy remains constant at every point in the oscillation cycle, as energy is continuously converted between kinetic and potential forms while the system's total energy is conserved.

In simple harmonic motion, the total mechanical energy is the sum of kinetic and potential energy. The potential energy is given by U = 0.5 * k * x^2. At the maximum displacement (amplitude A), the potential energy reaches its maximum value of 0.5 * k * A^2. Since the total energy is conserved, it is directly proportional to the square of the amplitude.

In an ideal Simple Harmonic Motion system without friction or air resistance, the total mechanical energy is the sum of kinetic and potential energy. This total energy remains constant throughout the entire cycle of motion, as energy is continuously converted between kinetic and potential forms. Therefore, the total energy is the same at every point in the path of the oscillator.

In simple harmonic motion, the total mechanical energy is the sum of the kinetic and potential energies. The potential energy is given by U = 0.5 * k * x^2, where x is the displacement. At the maximum displacement (amplitude A), the potential energy is 0.5 * k * A^2. Since the total energy remains constant throughout the motion, it is directly proportional to the square of the amplitude.

Kinetic energy is maximum at the equilibrium position (mean position) in SHM. At this point, the displacement from equilibrium is zero. Since potential energy (1/2kx²), restoring force (-kx), and acceleration (-ω²x) are all functions of displacement, they all become zero when the displacement is zero. This confirms that at the mean position, the system possesses maximum kinetic energy and zero potential energy.