10. Simple Harmonic Motion

 

Periodic Motion: When something moves in a way that it repeats itself regularly over time, it's called periodic or harmonic motion. Think of the hands of a clock, the Earth orbiting the sun, or the needle of a sewing machine—they all move in patterns that repeat.

Oscillatory Motion: If a particle keeps going back and forth around a fixed point in a regular pattern, it's called oscillatory or vibratory motion. Picture the motion of a piston in a car engine or the balance wheel of a watch—they move within specific limits, going back and forth.

Time Period: The time it takes for one complete back-and-forth motion is called the time period. It's basically how long it takes for the motion to start all over again.

Frequency: Frequency tells us how many back-and-forth motions happen in a certain amount of time. It's measured in Hertz, and it's related to the time period—if you know one, you can figure out the other.

Simple Harmonic Motion: When something moves back and forth around a fixed point in a way where its acceleration is directly related to how far it is from that point, it's called simple harmonic motion. The fixed point is called the equilibrium point—it's like the middle or resting position for the motion.

Characteristics of Simple Harmonic Motion:

1. 1. When a particle undergoes SHM, it passes through the middle position (mean position).

   • -No force acts on the particle.
   • -The acceleration of the particle is zero.
   • -The velocity is at its maximum.
   • -The kinetic energy of the particle is at its maximum.
   • -The potential energy is zero.

2. 2. When a particle undergoing SHM reaches the extreme end:

   • -The acceleration of the particle is at its maximum.
   • -The restoring force acting on the particle is at its maximum.
   • -The velocity of the particle is zero.
   • -The kinetic energy of the particle is zero.
   • -The potential energy is at its maximum.

Simple Pendulum: A simple pendulum consists of a small mass (called a bob) suspended from a fixed support by a light, inextensible string. The time period of oscillation of a simple pendulum is given by the formula: $�=2�\sqrt{\frac{�}{�}}$ Where:

T is the time period of oscillation,

l is the effective length of the pendulum,

g is the acceleration due to gravity.