Final answer:
The equation representing simple harmonic motion should show that acceleration is directly proportional to displacement and in the opposite direction. Option D, Acceleration = kx, is the closest, but to fully match SHM, it should be Acceleration = −kx, which is not listed.
Step-by-step explanation:
The question asks which one of the following equations of motion represents simple harmonic motion (SHM):
- Acceleration = −k₀x+k₁x²
- Acceleration = −k(x+a)
- Acceleration = k(x+a)
- Acceleration = kx
The defining characteristic of SHM is that the acceleration is directly proportional to the displacement and is in the opposite direction (sometimes referred to as Hooke's law). This is represented by the equation a(t) = −(k/m)x, where a(t) is acceleration, k is the spring constant, m is the mass, and x is the displacement.
Reviewing the choices, the one that fits this criterion is D. Acceleration = kx. However, to represent SHM fully and match the directionality indicated by Hooke's law, there should be a negative sign (as opposite direction to the displacement is a key feature).
Thus, the correct representation of SHM should be Acceleration = −kx, which is none of the options provided. If we are strictly looking for the form that matches the requirements of SHM (ignoring the missing negative sign), D is the closest option.
Therefore answer is D. Acceleration = kx.