This problem tests energy conservation in simple harmonic oscillators at extreme positions. In SHM on a frictionless surface, total mechanical energy remains constant throughout the motion. At equilibrium, the block has maximum speed with 20 J of kinetic energy and zero spring potential energy, establishing total energy as 20 J. At maximum displacement where the block is momentarily at rest, all kinetic energy transforms into spring potential energy, so the spring stores all 20 J. Choice D incorrectly suggests energy is lost when velocity is zero, but energy simply changes form rather than disappearing. When solving SHM problems, identify total energy at any point and apply conservation to find energies at other positions.

This question tests energy statements at a specific position in simple harmonic motion for a cart-spring system. Total mechanical energy E is constant, exchanging between K and U. At x = A/√2, U = E/2 and K = E/2, as $(x/A)^2$ = 1/2. Thus, kinetic equals potential energy there. Distractor C incorrectly suggests total E is greater than at x=0, but conservation keeps it constant. Calculate the position's $(x/A)^2$ fraction to determine energy equality or ratios in SHM problems.

This question assesses energy changes immediately after equilibrium in simple harmonic motion for a cart-spring system. In frictionless SHM, total energy is conserved, but K and U exchange as the cart oscillates. After passing equilibrium moving away, K decreases as speed slows, while U increases as the spring stretches or compresses. This continues until the turning point where K=0 and U maximum. Distractor B wrongly claims K stays maximum until the turning point, ignoring the continuous energy transfer. A transferable approach is to consider the direction of motion and position to predict whether K is increasing or decreasing in SHM.

This problem tests understanding of energy states in simple harmonic oscillators at turning points. In undamped SHM, total mechanical energy remains constant as kinetic and potential energies continuously interchange. At equilibrium, the mass has 6 J of kinetic energy and zero spring potential energy. At a turning point, the mass is instantaneously at rest, meaning velocity and kinetic energy are both zero. All 6 J of total energy is stored as spring potential energy at this position. Choice C incorrectly claims total energy is zero when both energies are zero, not recognizing that potential energy is maximum when kinetic energy is zero. When analyzing SHM at turning points, remember that zero velocity means zero kinetic energy, not zero total energy.

This question examines energy distribution in simple harmonic oscillators at different positions. In frictionless SHM, total mechanical energy (14 J) remains constant while kinetic and potential energies exchange. At equilibrium, all 14 J is kinetic energy (K = 14 J, U = 0 J). At maximum displacement where the cart is momentarily at rest, all energy converts to spring potential energy (K = 0 J, U = 14 J), making U > K at this position. Choice A incorrectly claims kinetic energy is greater at maximum displacement, when actually the cart is at rest there. To analyze SHM energy comparisons, identify where speed is maximum (equilibrium) versus zero (turning points).

This question assesses energy distribution at equilibrium in simple harmonic oscillators. In frictionless SHM, total mechanical energy stays constant, comprising kinetic and potential components that interchange. At equilibrium (x=0), the spring is unstretched, minimizing potential energy, while the mass's maximum speed maximizes kinetic energy. As it moves outward, kinetic energy decreases and potential increases, peaking at maximum displacement where kinetic is zero. Distractor B incorrectly asserts potential is maximum at equilibrium due to spring force, but force is zero there, and potential is actually minimum. A key strategy is to use conservation of energy to predict that maximum kinetic occurs where potential is minimum, and vice versa.

This question examines energy conservation in simple harmonic oscillators at different positions. In frictionless SHM, total mechanical energy remains constant as energy continuously transforms between kinetic and potential forms. At equilibrium, the system has 5 J of kinetic energy and zero spring potential energy, establishing total energy as 5 J. At the turning point where the mass is at rest, all kinetic energy converts to spring potential energy, so the spring stores all 5 J. Choice C incorrectly claims total energy is zero when speed is zero, confusing kinetic energy with total energy. To solve SHM energy problems, recognize that total energy equals the sum of kinetic and potential energies at any instant.

This problem tests understanding of energy conservation in simple harmonic oscillators. In undamped SHM, total mechanical energy remains constant as kinetic and potential energies continuously exchange. At equilibrium, the system has 9 J of kinetic energy and zero spring potential energy, establishing total mechanical energy as 9 J. This total energy remains constant throughout the motion, including at maximum displacement where all energy is potential. Choice D incorrectly suggests energy is lost at turning points, but in SHM without damping, energy is conserved. When solving SHM problems, recognize that total energy can be calculated at any convenient point and remains the same everywhere.

This question evaluates energy changes during motion in simple harmonic oscillators. In SHM with negligible friction, total mechanical energy remains constant as kinetic energy converts to potential and back. From equilibrium to a turning point, the increasing displacement raises potential energy, while decreasing speed lowers kinetic energy. At the turning point, all energy is potential, with kinetic at zero. Choice C is a distractor, wrongly suggesting both increase, but they cannot both rise since total energy is fixed. A transferable approach is to analyze energy trends based on position and velocity changes along the path of motion.

This problem involves energy conservation in simple harmonic oscillators. For frictionless SHM, total mechanical energy remains constant at K + U = 9 J (from equilibrium values). At maximum displacement, the mass has zero speed, which means kinetic energy K = 0 J. By energy conservation, all 9 J must be stored as potential energy in the spring, so U = 9 J. Choice A incorrectly claims kinetic energy is larger at maximum displacement, when actually kinetic energy is zero there because the mass is momentarily stationary. The strategy is to recognize that at turning points (maximum displacement), all energy is potential since velocity equals zero.