Question

part a

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

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

Explanation:

Analyze the restoring force in simple harmonic motion

Using the Simple Harmonic Motion Acceleration knowledge point

$$ F = -kx $$

$$ a = \frac{F}{m} = -\frac{k}{m}x $$

Determine acceleration at maximum displacement

Using the Simple Harmonic Motion Acceleration knowledge point

$$ |x| = A \implies |a| = \frac{k}{m}A = a_{\text{max}} $$

At maximum displacement, the magnitude of the instantaneous acceleration is also at its maximum.

Answer:

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