Question

In simple harmonic motion, the speed is greatest at that point in the cycle when
A) the magnitude of the acceleration is a maximum.
B) the displacement is a maximum.
C) the magnitude of the acceleration is a minimum.
D) the potential energy is a maximum.
E) the kinetic energy is a minimum.

Answer 1

Concepts and reason

The main concepts required to solve this problem are the simple harmonic motion, acceleration, displacement, potential energy, kinetic energy and speed.

Initially, Use the concepts of the simple harmonic motion, acceleration, kinetic energy, potential energy and explain all the incorrect statements and finally decide the correct statement from the given statements in the question.

Fundamentals

Simple harmonic motion can be defined as the type of periodic motion in which the restoring force is directly proportional to the displacement and acts in the direction opposite to the displacement, that is,

Here, k is the force constant, and y is the displacement.

Kinetic energy can be defined as the energy possessed by an object due to its motion.

The potential energy can be defined as the energy possessed by an object due to its position.

In simple harmonic motion, the magnitude of the acceleration is a maximum at the extreme position where the velocity becomes zero.

Therefore, the statement “The magnitude of the acceleration is a maximum” is incorrect.

The displacement is a maximum at the extreme position of the simple harmonic motion. Here; the speed is zero, which is a minimum.

Therefore, the statement “The displacement is a maximum” is incorrect.

The potential energy is a maximum at the extreme position of the simple harmonic motion as the vertical displacement is a maximum. At the extreme position, the speed is zero which is a minimum.

Therefore, the statement “The potential energy is a maximum” is incorrect.

The kinetic energy depends on the speed of the mass; the kinetic energy is a minimum at the extreme position of the simple harmonic motion, because the speed is a minimum.

Therefore, the statement “The kinetic energy is a minimum” is incorrect.

In simple harmonic motion, at the mean position, the acceleration is a minimum, and the displacement is also zero which is a minimum. Therefore, at the mean position of the simple harmonic motion, the speed will be more.

Therefore, the statement “The magnitude of the acceleration is a minimum” is a correct.

Ans:

The magnitude of the acceleration is a minimum.