Which statement correctly describes the speed of a mass on a horizontal spring during simple harmonic motion?

• A. The speed is maximum at the turning points where displacement is greatest.
• B. The speed is zero at equilibrium and maximum at extremes.
• C. The speed is zero at extremes and maximum at equilibrium.
• D. The speed is constant throughout the motion.

Answer: (C)

In simple harmonic motion, the mass continually exchanges potential energy stored in the spring with kinetic energy of the mass. At the turning points, the spring is at maximum stretch or compression, so all the energy is potential and the mass momentarily stops, giving zero speed. As the mass passes through the equilibrium position, the spring is neither stretched nor compressed, so most of the energy is kinetic and the speed reaches its maximum.

Mathematically, with x = A cos(ωt) we get v = dx/dt = -Aω sin(ωt). The speed is zero when sin(ωt) = 0 (at the turning points) and reaches its maximum magnitude when sin(ωt) = ±1 (at equilibrium). Hence the correct statement is that the speed is zero at extremes and maximum at equilibrium.