A motion repeating itself in an equal time interval is referred to as periodic or oscillatory motion.
When an object oscillates about a fixed position (mean position) its acceleration is directly proportional to its displacement from the mean position and is always directed towards the mean position, its motion is called SHM.
a ∝ –x
a=-kx
where k is spring constant.
Many phenomena include electromagnetic waves, alternating current circuits, musical instruments, bridges, and molecular motion that executes the simple harmonic motion.
A simple pendulum is a mass attached to a string or rod that swings back and forth under the influence of gravity.
When the bob of the pendulum is displaced at a small angle (θ) to an extreme position.Two forces that act upon a displaced pendulum:
The weight is further resolved into its component mgsinθ and mgcos θ.
A simple pendulum consists of a point mass suspended by a weightless string from a rigid support.
When the bob is displaced by a distance “x” to position “A,” work is done (Fd = Fx) to restore the bob with a force equal in magnitude but opposite in direction to the applied force “F.”
At position “A,” the bob gains maximum potential energy before being released, initiating periodic motion around the mean position “O.” The potential energy is greatest at points “A” and “B,” while the kinetic energy is maximum at position “O” due to the highest velocity.
As the bob moves from “O” to “A” or “O” to “B,” its velocity decreases, resulting in a negative acceleration, which becomes zero at the extreme position. Thus, the acceleration of the bob is directly proportional to the displacement but in the opposite direction. Consequently, the motion of a simple pendulum follows Simple Harmonic Motion (SHM).
The time period of simple pendulum can be calculate as follow:
T = 2π √L/g
where,
L= lenght of simple acceleration
g= acceleration due to gravity
In a ball and bowl system, a ball placed in a bowl-shaped hollow move back and forth inside when displaced. This motion is Simple Harmonic Motion (SHM), like a swinging pendulum. The ball experiences a force pulling it back to the center, proportional to its displacement, creating repetitive back-and-forth motion. Many natural systems exhibit SHM, making it an important concept in understanding various phenomena.
A damped system is a mechanical system that experiences a dissipation of energy, causing the amplitude of its oscillations to decrease over time.
Damped oscillation refers to the repetitive back-and-forth motion of a system that experiences a gradual reduction in amplitude due to the dissipation of energy.