(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

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

(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 $k_{eq}$: $T = 2\pi \sqrt{\frac{m(kL + YA)}{kYA}}$.

Class 11 Physics Oscillations SHM of Spring Mass System

Difficult

$A$ 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?

A
$2\pi \sqrt{\frac{m}{k}}$
B
$2\pi \sqrt{\frac{mYA}{kL}}$
C
$2\pi \sqrt{\frac{mk}{YA}}$
D
$2\pi \sqrt{\frac{m(kL + YA)}{kYA}}$

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$A$ 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?

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$A$ silver atom in a solid oscillates in simple harmonic motion in a specific direction with a frequency of $10^{12} \ s^{-1}$. What is the force constant of the bonds connecting one atom to the others? (Molar mass of silver $= 108 \ g/mol$ and Avogadro number $= 6.02 \times 10^{23} \ mol^{-1}$)

Two springs of force constants $300 \, N/m$ (Spring $A$) and $400 \, N/m$ (Spring $B$) are joined together in series. The combination is compressed by $8.75 \, cm$. The ratio of energy stored in $A$ and $B$ is $\frac{E_A}{E_B}$. Then $\frac{E_A}{E_B}$ is equal to

The potential energy of a particle of mass $0.02 \ kg$ moving along the $x$-axis is given by $V = A x(x-4) \ J$, where $x$ is in metres and $A$ is a constant. Which of the following is/are correct statement$(s)$?

The frequency of oscillations of a mass $m$ connected horizontally by a spring of spring constant $k$ is $4 \ Hz$. When the spring is replaced by two identical springs connected in series as shown in the figure,the effective frequency is:

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