Which among the following is the necessary condition for simple harmonic motion?

Simple Harmonic Motion (SHM) is a specific type of periodic motion defined by a unique relationship between acceleration and displacement. The fundamental necessary condition for SHM is that the restoring force, and consequently the acceleration, must be directly proportional to the displacement of the object from its equilibrium position [t1][t5]. Mathematically, this is expressed as a ∝ -x, where the negative sign indicates that the acceleration is always directed toward the equilibrium position, opposite to the direction of displacement [t2][t6]. While SHM does have a constant period [c1][c4], this is a characteristic property rather than the defining mechanical condition. Constant acceleration (Option 2) describes uniform linear motion, not oscillatory motion [c2]. In rotational SHM, torque is proportional to angular displacement, but for general SHM, the linear relationship between displacement and acceleration is the standard defining condition [t6][t8].

Sources

1. [1] Science-Class VII . NCERT(Revised ed 2025) > Chapter 8: Measurement of Time and Motion > In a Nutshell > p. 118
2. [2] Science-Class VII . NCERT(Revised ed 2025) > Chapter 8: Measurement of Time and Motion > THINK LIKE A SCIENTIST! > p. 110
3. [3] Science-Class VII . NCERT(Revised ed 2025) > Chapter 8: Measurement of Time and Motion > 8.4 Uniform and Non-uniform Linear Motion > p. 117