A wire of length L,cross-sectional area A,and | vedclass

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

Question

(D) The wire acts as a spring with an effective spring constant $k_1 = \frac{YA}{L}$.The spring with force constant $k_2 = k$ is connected in series w

Vedclass · Accepted Answer

$2\pi \sqrt{\frac{m(kL + YA)}{kYA}}$

Vedclass · Answer

(D) The wire acts as a spring with an effective spring constant $k_1 = \frac{YA}{L}$.The spring with force constant $k_2 = k$ is connected in series with the wire.The equivalent spring constant $k_{eq}$ for two springs in series is given by $\frac{1}{k_{eq}} = \frac{1}{k_1} + \frac{1}{k_2}$.Substituting the values: $\frac{1}{k_{eq}} = \frac{L}{YA} + \frac{1}{k} = \frac{kL + YA}{kYA}$.Therefore,$k_{eq} = \frac{kYA}{kL + YA}$.The time period $T$ of the mass-spring system is $T = 2\pi \sqrt{\frac{m}{k_{eq}}}$.Substituting $k_{eq}$: $T = 2\pi \sqrt{\frac{m(kL + YA)}{kYA}}$.

$A$ wire of length $L$,cross-sectional area $A$,and Young's modulus $Y$ is suspended,and a spring of force constant $k$ is attached to its lower end. If a mass $m$ is suspended from the spring and set into oscillations,what will be the time period of the system?

Similar Questions

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 scale of a spring balance which can measure from $0$ to $15 \ kg$ is $0.25 \ m$ long. If a body suspended from this balance oscillates with a time period $\frac{2 \pi}{5} \ s$,neglecting the mass of the spring,find the mass of the body suspended. (in $kg$)

If a spring has time period $T$,and is cut into $n$ equal parts,then the time period of each part 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 ... $\sec$.

$A$ mass $m$ is vertically suspended from a spring of negligible mass; the system oscillates with a frequency $n$. What will be the frequency of the system if a mass $4m$ is suspended from the same spring?

Vedclass Test Series

Exam Paper Generator

Online Exam Module