Which type of motion occurs when a restoring force is opposite to and proportional to a displacement?

Which type of motion occurs when a restoring force is opposite to and proportional to a displacement?

• A. Simple harmonic motion
• B. Linear motion
• C. Circular motion
• D. Rotational motion

Answer: (A)

The concept of a restoring force being opposite to and proportional to a displacement is a fundamental characteristic of simple harmonic motion. In simple harmonic motion, when an object is displaced from its equilibrium position, the restoring force tries to bring the object back to that position. This relationship can be mathematically described by Hooke's Law, which states that the force exerted by a spring (or any other system that undergoes simple harmonic motion) is proportional to the displacement from its equilibrium position and acts in the opposite direction. For instance, if a mass attached to a spring is pulled down and released, the spring will exert an upward force that increases with greater displacements. This results in oscillatory motion about the equilibrium position, producing the unique characteristics of simple harmonic motion, including constant frequency and a sinusoidal pattern over time. In contrast, linear motion refers to motion along a straight path without any restoring force acting towards an equilibrium position. Circular motion involves movement along a circular path and does not incorporate a restoring force concept. Rotational motion is associated with the rotation of objects around an axis, which is also distinct from the characteristics of simple harmonic motion. Therefore, the answer is clearly related to the principles governing simple harmonic motion, highlighting the role of restoring forces

The concept of a restoring force being opposite to and proportional to a displacement is a fundamental characteristic of simple harmonic motion. In simple harmonic motion, when an object is displaced from its equilibrium position, the restoring force tries to bring the object back to that position. This relationship can be mathematically described by Hooke's Law, which states that the force exerted by a spring (or any other system that undergoes simple harmonic motion) is proportional to the displacement from its equilibrium position and acts in the opposite direction.

For instance, if a mass attached to a spring is pulled down and released, the spring will exert an upward force that increases with greater displacements. This results in oscillatory motion about the equilibrium position, producing the unique characteristics of simple harmonic motion, including constant frequency and a sinusoidal pattern over time.

In contrast, linear motion refers to motion along a straight path without any restoring force acting towards an equilibrium position. Circular motion involves movement along a circular path and does not incorporate a restoring force concept. Rotational motion is associated with the rotation of objects around an axis, which is also distinct from the characteristics of simple harmonic motion. Therefore, the answer is clearly related to the principles governing simple harmonic motion, highlighting the role of restoring forces