A simple harmonic oscillator consists of a pa | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The initial time period of the simple harmonic oscillator is given by $T = 2 \pi \sqrt{\frac{m}{k}}$.When a spring of length $l$ and spring consta

Vedclass · Accepted Answer

$\frac{T}{\sqrt{2}}$

Vedclass · Answer

(C) The initial time period of the simple harmonic oscillator is given by $T = 2 \pi \sqrt{\frac{m}{k}}$.When a spring of length $l$ and spring constant $k$ is cut into two equal parts,the length of each part becomes $l' = \frac{l}{2}$.Since the spring constant $k$ is inversely proportional to the length of the spring $(k \propto \frac{1}{l})$,the new spring constant $k'$ for each part will be $k' = 2k$.Substituting the new spring constant into the time period formula,we get the new time period $T' = 2 \pi \sqrt{\frac{m}{k'}} = 2 \pi \sqrt{\frac{m}{2k}}$.This simplifies to $T' = \frac{1}{\sqrt{2}} \left( 2 \pi \sqrt{\frac{m}{k}} \right) = \frac{T}{\sqrt{2}}$.

$A$ simple harmonic oscillator consists of a particle of mass $m$ and an ideal spring with spring constant $k$. The particle oscillates with a time period $T$. The spring is cut into two equal parts. If one part oscillates with the same particle,the time period will be

Similar Questions

Which two distinct microbial processes are responsible for the release of fixed nitrogen as dinitrogen gas $(N_2)$ to the atmosphere?

The ends of an element of zinc wire are kept at a small temperature difference $\Delta T$ and a small current $I$ is passed through the wire. Then,the heat developed per unit time

In an $n$-type semiconductor,the Fermi energy level lies

High purity copper metal is obtained by

Which process is used to obtain products like cheese and yogurt?

Vedclass Test Series

Exam Paper Generator

Online Exam Module