TRUE OR FALSE The motion of a pendulum for which the maximum displacement from equilibrium varies is an example of simple harmonic motion.
No, not if it varies. It could be harmonic motion with damping. I am not really certain what the statement means.
True. The motion of a pendulum, where the maximum displacement from equilibrium varies, is still an example of simple harmonic motion. Simple harmonic motion refers to any motion that follows a certain pattern in which the force or acceleration is directly proportional to displacement but in the opposite direction. While the amplitude (maximum displacement) may change, if the force acting on the pendulum is proportional to the displacement and directed towards the equilibrium position, it still qualifies as simple harmonic motion.
To determine whether the statement is true or false, we need to understand the concept of simple harmonic motion and analyze the motion of the pendulum.
Simple harmonic motion refers to a type of periodic motion where an object oscillates back and forth around an equilibrium position, and its displacement from the equilibrium position is directly proportional to the restoring force acting on it. In simple terms, it is a smooth swinging or vibrating motion.
In the case of a pendulum, it consists of a mass (known as the bob) hanging from a fixed point and swinging freely. When the pendulum is displaced from its equilibrium position, it experiences a restoring force (gravity in this case) that makes it swing back towards the equilibrium position.
Now, let's analyze the statement "The motion of a pendulum for which the maximum displacement from equilibrium varies is an example of simple harmonic motion."
If the maximum displacement from equilibrium (amplitude) of the pendulum varies, it means that the amplitude changes over time as the pendulum swings. In such a case, the restoring force acting on the pendulum will not be directly proportional to its displacement.
According to the definition of simple harmonic motion, the maximum displacement from equilibrium should remain constant, as the restoring force is directly proportional to the displacement. Therefore, if the maximum displacement from equilibrium varies, it means that the motion of the pendulum is not an example of simple harmonic motion.
Hence, the statement "The motion of a pendulum for which the maximum displacement from equilibrium varies is an example of simple harmonic motion" is FALSE.