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

Question

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 (A) 2 T (B) √2 T (C) (T/√2) (D) (T/2)

Tardigrade Admin · Accepted Answer

Time period of oscillator, T=2 π √(m/k) As k propto (1/l) (where, l is the length of spring) ∵ k'=2 k ∴ T'=2 π √(m/2 k) =(1/√2) T

Q. 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

$2 T$

$2 T$

$\frac{T}{2}$

$\frac{T}{2}$

Time period of oscillator,
$T = 2 π \frac{m}{k}$
As $k \propto \frac{1}{l}$ (where, $l$ is the length of spring)
$∵ k^{'} = 2 k$
$∴ T^{'} = 2 π \frac{m}{2 k}$
$= \frac{1}{2} T$

Q. 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

2T

2​T

2​T​

2T​

Time period of oscillator, T=2πkm​​ As k∝l1​ (where, l is the length of spring) ∵k′=2k ∴T′=2π2km​​ =2​1​T

Q. 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

$2 T$

$2 T$

$\frac{T}{2}$

$\frac{T}{2}$

Time period of oscillator,
$T = 2 π \frac{m}{k}$
As $k \propto \frac{1}{l}$ (where, $l$ is the length of spring)
$∵ k^{'} = 2 k$
$∴ T^{'} = 2 π \frac{m}{2 k}$
$= \frac{1}{2} T$