What kind of motion makes the pendulum when the amplitudes are small ????
periodic?
When the amplitudes (the maximum displacement from the equilibrium position) of a pendulum are small, it exhibits simple harmonic motion (SHM). To understand this type of motion, we need to consider a few key concepts.
A pendulum consists of a mass (called the bob) attached to a fixed point by a string or rod. When the bob is displaced from its equilibrium position and released, it undergoes oscillations. The nature of these oscillations depends on the amplitude.
In the case of small amplitudes, the motion of the pendulum is approximately simple harmonic. Simple harmonic motion is a type of oscillatory motion where the restoring force acting on the mass is directly proportional to the displacement from the equilibrium position, and it always acts towards the equilibrium.
To determine what kind of motion the pendulum makes when the amplitudes are small, we can follow these steps:
1. Set up the equation: The equation that governs the motion of a simple pendulum is given by:
T = 2π √(L / g)
where T is the period of the pendulum, L is the length of the string or rod, and g is the acceleration due to gravity.
2. Calculate the period: For small amplitudes, we can approximate the period using the formula:
T ≈ 2π √(L / g)
Here, T represents the time taken for one complete cycle of oscillation.
3. Analyze the motion: With the period determined, we find that the pendulum oscillates back and forth in a regular pattern around the equilibrium position. The motion is characterized by the pendulum bob swinging from one side to the other, moving back to the opposite side, and so on. This motion is repetitive and periodic.
Therefore, when the amplitudes of a pendulum are small, the pendulum exhibits simple harmonic motion, swinging back and forth around its equilibrium position in a regular and repetitive pattern.