A mass in the diagram below undergoes simple harmonic When the mass reaches point x = 0 its instantaneous acceleration is:

Question

BlackTom AI · Accepted Answer

The problem asks about the instantaneous acceleration of a mass undergoing simple harmonic motion at the instant when its displacement is x = 0.
Option 1: 'Maximum and can be positive or negative' — In SHM, acceleration a = -ω^2 x, so acceleration is proportional to and opposite the displacement. At x = 0, a = -ω^2(0) = 0. Therefore this statement is incorrect.
Option 2: 'Zero' — This matches the SHM relation a = -ω^2 x, since x = 0 yields a = 0. This is the correct behavior for the acceleration at the equilibrium position, so this option is correct.
Option 3: 'Less than maximum' — The concept of 'maximum' acceleration occurs at the maximum displacement (|x| = A), where |a| = ω^2 A. At x = 0, the acceleration is exactly zero, which is not merely less than maximum but actually zero. Thus this option is inaccurate.
Option 4: 'Constant and doesn’t depend on the location' — In SHM, acceleration depends on position via a = -ω^2 x. Since a changes with x, this statement is false.

SPHY001 Practice Quiz - Unit 16 | LA056

A mass in the diagram below undergoes simple harmonic When the mass reaches point x = 0 its instantaneous acceleration is:

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