ewce09.azraftaohid.me/L1T2/PHY 101/SB/Notes/Simple harmonic motion.md

Created: 2023-11-24T17:04:00

Oscillatory motion that i) has a constant amplitude, ii) sinusoidal displacement function, and iii) has a restoring force acting directly proportional to the displacement from equilibrium position and is directed towards it. In essence, it is a oscillatory motion that has non-constant velocity (apart from being a sinusoidal func).

E.g., a simple pendulum (angular motion), a mass-spring system (linear motion).

Constraints on SHM,

1. Fixed time repetition (defines periodic motion)
2. Fixed point repetition (defines oscillatory motion)
3. Acceleration is directly proportional to displacement from equilibrium position
4. Acceleration direction is towards equilibrium (or opposite of displacement)

3 & 4 -> $a\propto x$ & $a=-\mathbf{x}$

Forces impacting SHM:

1. Newtonian force:$$F_n=ma$$
2. Damping force (friction): Opposes the motion of the body. Directly proportional and opposite of velocity. $$F_D=-bv$$
3. Hooke force: $$F_H=-kx$$