At x = 0, which statement about a mass on a spring is true?

At x = 0, which statement about a mass on a spring is true?

• A. Restoring force = max; acceleration = max; Potential energy = max; kinetic energy = 0
• B. Restoring force = 0; acceleration = 0; Potential energy = 0; kinetic energy = max
• C. Restoring force = 0; acceleration = 0; Potential energy = max; speed = 0
• D. Restoring force = 0; acceleration = max; Potential energy = max; speed = 0

Answer: (B)

At x = 0, the spring is at its natural length, so the restoring force is zero: F = -kx = 0. With no force, the acceleration a = F/m is also zero. The potential energy stored in the spring is (1/2)kx^2, which is zero when x = 0. But the mass is moving fastest through this position in simple harmonic motion, so the kinetic energy is at its maximum: K = (1/2)mv^2 is largest there. So the statement that best fits is: zero restoring force, zero acceleration, zero potential energy, and maximum kinetic energy at the equilibrium position. The other descriptions describe different moments of the motion (like the farthest points where speed is zero and potential energy is maximum, or moments with nonzero force and nonzero acceleration).

At x = 0, the spring is at its natural length, so the restoring force is zero: F = -kx = 0. With no force, the acceleration a = F/m is also zero. The potential energy stored in the spring is (1/2)kx^2, which is zero when x = 0. But the mass is moving fastest through this position in simple harmonic motion, so the kinetic energy is at its maximum: K = (1/2)mv^2 is largest there.

So the statement that best fits is: zero restoring force, zero acceleration, zero potential energy, and maximum kinetic energy at the equilibrium position. The other descriptions describe different moments of the motion (like the farthest points where speed is zero and potential energy is maximum, or moments with nonzero force and nonzero acceleration).