(D) In the given figure,the mass $m$ is attached to two springs in parallel. When the mass is displaced vertically,both springs experience the same di

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$2\pi \sqrt{\frac{m}{k_1 + k_2}}$

(D) In the given figure,the mass $m$ is attached to two springs in parallel. When the mass is displaced vertically,both springs experience the same displacement. For springs in parallel,the equivalent force constant $k_{eq}$ is the sum of the individual force constants: $k_{eq} = k_1 + k_2$ The time period $T$ of a spring-mass system is given by the formula: $T = 2\pi \sqrt{\frac{m}{k_{eq}}}$ Substituting the value of $k_{eq}$: $T = 2\pi \sqrt{\frac{m}{k_1 + k_2}}$ Therefore,the correct option is $(D)$.

Class 11 Physics Oscillations SHM of Spring Mass System

Easy

$A$ mass $m$ is suspended by means of two coiled springs which have the same length in the unstretched condition,as shown in the figure. Their force constants are $k_1$ and $k_2$ respectively. When set into vertical vibrations,the period will be:

A
$2\pi \sqrt{\frac{m}{k_1 k_2}}$
B
$2\pi \sqrt{m \frac{k_1}{k_2}}$
C
$2\pi \sqrt{\frac{m}{k_1 - k_2}}$
D
$2\pi \sqrt{\frac{m}{k_1 + k_2}}$

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SHM of Spring Mass System

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

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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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Medium

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MediumAP EAMCET 2025

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$A$ mass $m$ is suspended by means of two coiled springs which have the same length in the unstretched condition,as shown in the figure. Their force constants are $k_1$ and $k_2$ respectively. When set into vertical vibrations,the period will be:

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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

$A$ 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?

$A$ block of mass $m$ rests on a platform. The platform is given up and down $SHM$ with an amplitude $d$. What is the maximum frequency so that the block never leaves the platform?

$A$ flat horizontal board moves up and down in $SHM$ with an amplitude $\alpha$. What is the shortest permissible time period of the vibration such that an object placed on the board does not lose contact with the board?

$A$ body of mass $1 \ kg$ is suspended from a spring of force constant $600 \ N \ m^{-1}$. Another body of mass $0.5 \ kg$ moving vertically upwards hits the suspended body with a velocity of $3 \ m \ s^{-1}$ and gets embedded in it. The amplitude of motion is (in $cm$)

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