(A) When a block is connected to two springs on either side,any displacement $x$ of the block causes one spring to compress by $x$ and the other to st

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(A) When a block is connected to two springs on either side,any displacement $x$ of the block causes one spring to compress by $x$ and the other to stretch by $x$.Since both springs exert a restoring force in the same direction (opposing the displacement),the springs are effectively in a parallel configuration.The equivalent spring constant $K_{eq}$ is given by $K_{eq} = K_1 + K_2$.The angular frequency $\omega$ of a spring-mass system is given by $\omega = \sqrt{\frac{K_{eq}}{m}}$.Substituting the value of $K_{eq}$,we get $\omega = \sqrt{\frac{K_1 + K_2}{m}}$.

Class 11 Physics Oscillations SHM of Spring Mass System

Easy

$A$ block is placed on a frictionless horizontal table. The mass of the block is $m$ and springs are attached on either side with force constants $K_1$ and $K_2$. If the block is displaced a little and left to oscillate,then the angular frequency of oscillation will be

A
$[\frac{K_1 + K_2}{m}]^{1/2}$
B
$[\frac{K_1 K_2}{m(K_1 + K_2)}]^{1/2}$
C
$[\frac{K_1 K_2}{(K_1 - K_2)m}]^{1/2}$
D
$[\frac{K_1^2 + K_2^2}{(K_1 + K_2)m}]^{1/2}$

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SHM of Spring Mass System

Two particles $A$ and $B$ of equal masses are suspended from two massless springs of spring constants $k_1$ and $k_2$,respectively. If the maximum velocities during oscillations are equal,the ratio of amplitudes of $A$ and $B$ is

Medium

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$A$ pan with a set of weights is attached to a light spring. When disturbed,the mass-spring system oscillates with a time period of $0.6 \ s$. When some additional weights are added,the time period becomes $0.7 \ s$. The extension caused by the additional weights is approximately given by ......... $cm$.

Difficult

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$A$ block of mass $100 \,g$ is suspended vertically between two massless springs, each with a spring constant $k=1 \,N/m$. The block is hit from above to impart an impulse of $2 \,Ns$. Calculate the maximum displacement from the equilibrium position of the block. (Take $g=10 \,m/s^2$) (in $\,m$)

EasyTS EAMCET 2019

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Two masses $m_1$ and $m_2$ are suspended together by a massless spring of constant $K$. When the masses are in equilibrium,$m_1$ is removed without disturbing the system. The amplitude of oscillations is

Medium

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$A$ mass '$m$' attached to a spring oscillates with a period of $3 \ s$. If the mass is increased by $0.6 \ kg$,the period increases by $3 \ s$. The initial mass '$m$' is equal to (in $kg$)

MediumMHT CET 2024

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$A$ block is placed on a frictionless horizontal table. The mass of the block is $m$ and springs are attached on either side with force constants $K_1$ and $K_2$. If the block is displaced a little and left to oscillate,then the angular frequency of oscillation will be

Similar Questions

Two particles $A$ and $B$ of equal masses are suspended from two massless springs of spring constants $k_1$ and $k_2$,respectively. If the maximum velocities during oscillations are equal,the ratio of amplitudes of $A$ and $B$ is

$A$ block of mass $100 \,g$ is suspended vertically between two massless springs, each with a spring constant $k=1 \,N/m$. The block is hit from above to impart an impulse of $2 \,Ns$. Calculate the maximum displacement from the equilibrium position of the block. (Take $g=10 \,m/s^2$) (in $\,m$)

Two masses $m_1$ and $m_2$ are suspended together by a massless spring of constant $K$. When the masses are in equilibrium,$m_1$ is removed without disturbing the system. The amplitude of oscillations is

$A$ mass '$m$' attached to a spring oscillates with a period of $3 \ s$. If the mass is increased by $0.6 \ kg$,the period increases by $3 \ s$. The initial mass '$m$' is equal to (in $kg$)

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