A simple pendulum has mass 1.20 kg and length 0.700 m . (a) What is the period of the pendulum n

step 1 So here for Part A, we can say that the period of a simple pendulum, T would be equaling 2 pi, m

A simple pendulum has mass 1.20 kg and length 0.700 m . (a)...

A simple pendulum has mass 1.20 $\mathrm{kg}$ and length 0.700 $\mathrm{m} .$ (a) What is the period of the pendulum near the surface of Earth? (b) If the same mass is attached to a spring, what spring constant would result in the period of motion found in part (a)?

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Key Concepts

Simple Pendulum

A simple pendulum consists of a mass suspended from a fixed point by a string or rod, allowed to swing freely under the influence of gravity. For small angular displacements, its motion approximates simple harmonic motion, and the period depends only on the length of the pendulum and the acceleration due to gravity, not on the mass of the bob. This is captured by the formula T = 2??(L/g).

Spring-Mass Oscillator

A spring-mass system involves a block attached to a spring that obeys Hooke’s law, where the restoring force is proportional to the displacement from equilibrium. The system undergoes simple harmonic motion, and its period depends on both the mass and the spring constant, given by T = 2??(m/k). This concept connects how force and displacement determine oscillatory behavior in elastic systems.

Simple Harmonic Motion

Simple harmonic motion is a type of oscillatory motion where the restoring force is directly proportional to the displacement from an equilibrium position and acts in the opposite direction. It provides the foundational framework for understanding the dynamics of both the simple pendulum (in the small-angle approximation) and the spring-mass system, allowing us to predict their periodic behavior from their physical parameters.

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