What is the relationship between the period of a simple harmonic oscillator and
Practice Questions
Q1
What is the relationship between the period of a simple harmonic oscillator and its mass and spring constant?
T = 2π√(m/k)
T = 2π√(k/m)
T = m/k
T = k/m
Questions & Step-by-Step Solutions
What is the relationship between the period of a simple harmonic oscillator and its mass and spring constant?
Step 1: Understand what a simple harmonic oscillator is. It is a system that moves back and forth in a regular pattern, like a mass attached to a spring.
Step 2: Identify the two important factors in the formula: mass (m) and spring constant (k). The mass is how heavy the object is, and the spring constant measures how stiff the spring is.
Step 3: Learn the formula for the period (T) of the oscillator: T = 2π√(m/k). This means the period depends on both the mass and the spring constant.
Step 4: Notice that if the mass (m) increases, the period (T) also increases. This means it takes longer for the system to complete one full cycle.
Step 5: Observe that if the spring constant (k) increases, the period (T) decreases. A stiffer spring makes the system oscillate faster.
Step 6: Conclude that the period of a simple harmonic oscillator is directly related to the mass and inversely related to the spring constant.
