Question

part a

a mass on the end of a spring undergoes simple harmonic motion. at the instant when the mass is at its equilibrium position, what is its instantaneous acceleration?

• instantaneous acceleration cannot be determined without additional information.
• at equilibrium, its instantaneous acceleration is at maximum.
• at equilibrium, its instantaneous acceleration is zero.
• at equilibrium, its instantaneous acceleration is less than its maximum but not zero.

Explanation:

Identify the restoring force relation

Using the Simple Harmonic Motion Acceleration knowledge point

$$ F_{\text{net}} = -kx $$

Relate force to acceleration

Using the Simple Harmonic Motion Acceleration knowledge point

$$ a = -\frac{k}{m}x = -\omega^2 x $$

Evaluate acceleration at equilibrium

Using the Simple Harmonic Motion Acceleration knowledge point

$$
LATEXBLOCK0
$$

Answer:

• Instantaneous acceleration cannot be determined without additional information.
• At equilibrium, its instantaneous acceleration is at maximum.
• At equilibrium, its instantaneous acceleration is zero. (Correct answer)
• At equilibrium, its instantaneous acceleration is less than its maximum but not zero.