A spring-block system in horizontal oscillati | vedclass

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

Question

(C) The initial time period of the spring-block system is given by $T = 2 \pi \sqrt{\frac{m}{k}}$,where $k$ is the original spring constant.When a spr

Vedclass · Accepted Answer

$\frac{T}{2}$

Vedclass · Answer

(C) The initial time period of the spring-block system is given by $T = 2 \pi \sqrt{\frac{m}{k}}$,where $k$ is the original spring constant.When a spring is cut into $n$ equal parts,the spring constant of each part becomes $k' = n k$. Here,$n = 4$,so the new spring constant is $k' = 4 k$.The new time period $T'$ is given by $T' = 2 \pi \sqrt{\frac{m}{k'}} = 2 \pi \sqrt{\frac{m}{4 k}}$.Substituting $T = 2 \pi \sqrt{\frac{m}{k}}$,we get $T' = \frac{1}{2} 	imes (2 \pi \sqrt{\frac{m}{k}}) = \frac{T}{2}$.Thus,the new time period is $\frac{T}{2}$.

$A$ spring-block system in horizontal oscillation has a time period $T$. If the spring is cut into four equal parts and the block is re-connected with one of the parts,what will be the new time period of oscillation?

Similar Questions

All the springs in figures $(a)$,$(b)$,and $(c)$ are identical,each having a force constant $K$. $A$ mass $m$ is attached to each system. If $T_a, T_b$,and $T_c$ are the time periods of oscillations of the three systems in figures $(a)$,$(b)$,and $(c)$ respectively,then:

Two massless springs with spring constants $2k$ and $9k$ carry $50\,g$ and $100\,g$ masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then,the ratio of their respective amplitudes will be

$A$ $2\, kg$ block moving with $10\, m/s$ strikes a spring of constant $\pi^2\, N/m$ attached to a $2\, kg$ block at rest kept on a smooth floor. The time for which the moving block remains in contact with the spring will be ... $\sec$.

In the situation as shown in the figure,the time period of vertical oscillation of the block for small displacements will be:

Two identical springs are connected to a mass $m$ as shown in the figure ($k$ = spring constant). If the time period of the configuration in $(a)$ is $2 \,s$, what is the time period of the configuration in $(b)$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module