In a simple pendulum, the mass of the bob does not affect the amplitude, time period, or frequency of the pendulum's motion. This is known as the property of "isochronism" in simple pendulums.
The reason for this can be understood by examining the equation of motion for a simple pendulum. The equation is given by:
T = 2π√(L/g)
Where: T = time period of the pendulum L = length of the pendulum g = acceleration due to gravity
As you can see, the mass of the bob does not appear in this equation. This means that the time period (T) of the pendulum only depends on the length (L) and the acceleration due to gravity (g), not on the mass.
The reason for this independence of mass is because the restoring force acting on the pendulum is provided by gravity, which is proportional to the weight of the bob (mg). The component of weight acting as a restoring force is mg sin(theta), where theta is the angular displacement of the pendulum from its equilibrium position. The restoring force is directly proportional to sin(theta) and is independent of the mass. This is why the change in mass does not affect the amplitude, time period, or frequency of the simple pendulum.
However, it's important to note that this analysis assumes ideal conditions, such as a massless and inextensible string, small angles of oscillation, and the absence of air resistance. In real-world scenarios, where these assumptions may not hold, the mass of the bob can have some influence on the pendulum's motion.