Physics

Physics

Problem

Which of the following expressions corresponds to simple harmonic motion along a straight line, where x is the displacement and a, b, c are positive constants? a. a+bx−cx2a + bx - cx^2 b. a−bx+cx2a - bx + cx^2 c. bx2bx^2 d. −bx-bx
Intuitive explanation

Simple harmonic motion is fundamentally about restoring force proportional to displacement—the farther you go, the harder you're pulled back. The key is recognizing that a=−ω2xa = -\omega^2 x (acceleration equals a negative constant times position) is the mathematical signature of SHM. Look for expressions where acceleration or force depends linearly on displacement with a negative sign, not on velocity or higher powers of position.

Intuitive explanation

Simple harmonic motion is fundamentally about restoring force proportional to displacement—the farther you go, the harder you're pulled back. The key is recognizing that a=−ω2xa = -\omega^2 x (acceleration equals a negative constant times position) is the mathematical signature of SHM. Look for expressions where acceleration or force depends linearly on displacement with a negative sign, not on velocity or higher powers of position.

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