You do not care what force is applied at the point of suspension. You only care where that point is at time t, and how that affects the angle of the pendulum.LCSphysicist said:
A simple pendulum subject to a driven force is a physical system that consists of a mass attached to a fixed point by a string or rod and is subjected to an external driving force. The driving force can be periodic, such as a motor or a hand pushing the pendulum, or non-periodic, such as wind or friction.
The driving force affects the motion of a simple pendulum by changing its amplitude, frequency, and phase. The amplitude is the maximum displacement of the pendulum from its equilibrium position, the frequency is the number of oscillations per unit time, and the phase is the position of the pendulum at a specific time.
A simple pendulum subject to a driven force has various applications in science and engineering. It is used in clocks and watches to keep time, in seismology to measure earthquakes, and in laboratory experiments to study the effects of external forces on a system.
The motion of a simple pendulum subject to a driven force can be described mathematically using the equation of motion for a damped driven oscillator. This equation takes into account the effects of the driving force, damping, and the restoring force of the pendulum. It is a second-order differential equation that can be solved using various mathematical techniques.
The behavior of a simple pendulum subject to a driven force can be affected by various factors such as the amplitude and frequency of the driving force, the length and mass of the pendulum, and the presence of damping forces. The initial conditions, such as the starting position and velocity, also play a role in determining the motion of the pendulum.