Question
Prove that T=2π√m/k with little explanatory sentences
Answers
GPT 3.5
Given a mass-spring system with mass m and spring constant k, the period T of the system can be calculated using the formula T=2π√m/k.
First, determine the angular frequency ω of the system using the formula ω=√(k/m).
Next, find the period T by dividing 2π by the angular frequency ω, which gives T=2π/ω.
Substitute the angular frequency ω=√(k/m) into the formula and simplify to get T=2π√m/k.
Therefore, T=2π√m/k is the formula to calculate the period of a mass-spring system.
First, determine the angular frequency ω of the system using the formula ω=√(k/m).
Next, find the period T by dividing 2π by the angular frequency ω, which gives T=2π/ω.
Substitute the angular frequency ω=√(k/m) into the formula and simplify to get T=2π√m/k.
Therefore, T=2π√m/k is the formula to calculate the period of a mass-spring system.