Final answer:
The object suspended from a massless string most likely exhibits harmonic motion, swinging back and forth around the equilibrium position, which is when the pendulum is hanging straight down. The restoring force due to gravity is responsible for the pendulum's oscillatory behavior.
Step-by-step explanation:
When an object of weight W is suspended from the center of a massless string, the most likely outcome is that the object exhibits harmonic motion. A simple pendulum like this one consists of a small-diameter bob and a string that has a very small mass but is strong enough not to stretch appreciably. The equilibrium position of a pendulum is when the pendulum is hanging straight down. If the object is displaced and let go, it will move back towards this equilibrium position due to the restoring force from gravity. This restoring force causes the pendulum to oscillate back and forth, performing simple harmonic motion.
The equilibrium position of a pendulum occurs when the pendulum is hanging straight down, which corresponds to when the tension in the string is counteracted by the weight of the object, creating a condition where the net force on the object is zero. The restoring force is due to gravity pulling the mass directly downwards, while the string's tension pulls the mass towards the central vertical line (equilibrium position).
In the case of a pendulum placed into oscillatory motion as described in figures 15.20 and 5.40, we observe that as soon as a pendulum is displaced from its equilibrium position, it experiences a restoring force characterized by -mg sin(θ), where m is the mass of the bob, g is the acceleration due to gravity, and θ is the angle of displacement. This restoring force ensures that the pendulum will attempt to return to the equilibrium position, hence initiating an oscillating motion.