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 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 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 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.

This problem tests understanding of energy conservation in simple harmonic oscillators. In frictionless SHM, total mechanical energy remains constant throughout oscillation. At equilibrium, K = 2 J and U = 0 J, giving a total of 2 J. At maximum displacement where the mass is momentarily at rest, velocity equals zero, so kinetic energy K = 0 J. By conservation of energy, all 2 J must be stored as spring potential energy, making U = 2 J. Choice A incorrectly claims kinetic energy is maximum at maximum displacement, when it's actually zero there since the mass stops momentarily. Remember that in SHM, energy continuously exchanges between kinetic and potential forms while maintaining a constant total.

This question examines energy conservation in simple harmonic oscillators. In undamped SHM, mechanical energy is conserved, so the total K + U remains constant at 7 J (from equilibrium). At a turning point where speed equals zero, kinetic energy must be 0 J (since K = ½mv²). Therefore, all 7 J of mechanical energy exists as spring potential energy at the turning point. Choice C incorrectly suggests energy is lost at turning points, but energy only transforms between forms without being destroyed in conservative systems. To solve SHM energy problems, identify total energy from any known state and apply conservation to find energy distribution at other positions.

This problem tests understanding of energy conservation in simple harmonic oscillators. In SHM without friction, total mechanical energy remains constant throughout the motion. At equilibrium, all energy is kinetic (K₀), while at maximum displacement, the block is momentarily at rest so all energy converts to spring potential energy. Since total energy is conserved, the spring potential energy at maximum displacement must equal K₀. Choice A incorrectly states the block has maximum speed at maximum displacement, when actually speed is zero there. When solving SHM energy problems, remember that total mechanical energy stays constant, with continuous exchange between kinetic and potential forms.