A mass m performs oscillations of period T wh | vedclass

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

Question

(D) The time period of a spring-mass system is given by $T = 2\pi \sqrt{\frac{m}{K}}$.Initially,the time period is $T_1 = 2\pi \sqrt{\frac{m}{K}}$.Whe

Vedclass · Accepted Answer

$\frac{T}{2}$

Vedclass · Answer

(D) The time period of a spring-mass system is given by $T = 2\pi \sqrt{\frac{m}{K}}$.Initially,the time period is $T_1 = 2\pi \sqrt{\frac{m}{K}}$.When a spring of force constant $K$ is cut into two equal parts,the force constant of each part becomes $K' = 2K$.When these two springs are arranged in parallel,the equivalent force constant $K_{eq}$ is the sum of the individual force constants:$K_{eq} = K' + K' = 2K + 2K = 4K$.The new time period $T_2$ is given by $T_2 = 2\pi \sqrt{\frac{m}{K_{eq}}} = 2\pi \sqrt{\frac{m}{4K}}$.Comparing $T_2$ with $T_1$:$T_2 = \frac{1}{2} 	imes (2\pi \sqrt{\frac{m}{K}}) = \frac{T}{2}$.

$A$ mass $m$ performs oscillations of period $T$ when suspended by a spring of force constant $K$. If the spring is cut into two equal parts and arranged in parallel,and the same mass $m$ is oscillated by them,then the new time period will be:

Similar Questions

$A$ coin is placed on a horizontal platform. The platform performs vertical simple harmonic motion with an angular frequency $\omega$. The amplitude of oscillation is gradually increased. At what condition will the coin first lose contact with the platform?

Springs of spring constants $K, 2K, 4K, 8K, \dots$ are connected in series. $A$ mass of $40 \, g$ is attached to the lower end of the last spring and the system is allowed to vibrate. What is the time period of oscillation in seconds? (Given $K = 2 \, N/cm$)

The frequency of oscillation of the spring-mass system shown in the figure is:

How does the period of oscillation depend on the mass of the block attached to the end of a spring?

If $A$ is the area of cross-section of a spring,$L$ is its length,$E$ is the Young's modulus of the material of the spring,then the time period and force constant of the spring will be respectively:

Vedclass Test Series

Exam Paper Generator

Online Exam Module