Topic: Theory of Machines / Vibrations
Which of the following relationships between the force F on a particle and the particles position x implies simple harmonic oscillation
- A. $F = -7x$
- B. $F = -200x^{2}$
- C. $F = 10x$
- D. $F = 5x^{2}$
Answer: A. $F = -7x$
Explanation: The fundamental condition for simple harmonic oscillation is that the restoring force (F) on a particle must be directly proportional to its displacement (x) from the mean position and directed towards the mean position. This is represented mathematically as $F = -kx$, where k is a positive spring constant. Only option (a) matches this linear relationship.