(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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Oscillations

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SHM of Spring Mass System

Consider a spring-mass simple harmonic oscillator in one dimension. The mass of the particle is $m \text{ kg}$ and the spring constant is $k \text{ Nm}^{-1}$. At a given instant, the extension of the spring is $x \text{ m}$ and the speed of the particle is $v \text{ ms}^{-1}$. On the $x-v$ plane, if the graph of $v$ as a function of $x$ is a circle, then the correct option is:

DifficultNEET 2026

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$A$ mass of $2 \, kg$ is attached to a spring with a spring constant of $50 \, N/m$. The block is pulled to a distance of $5 \, cm$ from its equilibrium position at $x = 0$ on a horizontal frictionless surface and released from rest at $t = 0$. Write the expression for its displacement at any time $t$.

Medium

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Find the maximum amplitude (in $cm$) of the $SHM$ such that block $A$ will not slip on block $B$. Given: spring constant $K = 100 \ N/m$,mass of block $A$ $m_A = 0.25 \ kg$,mass of block $B$ $m_B = 1.25 \ kg$,and coefficient of friction between $A$ and $B$ is $\mu = 0.4$. Take $g = 10 \ m/s^2$.

DifficultAIIMS 2019

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$A$ spring has a certain mass suspended from it and its period for vertical oscillations is $T_1$. The spring is now cut into two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillations is now $T_2$. The ratio $T_1 / T_2$ is

DifficultMHT CET 2023

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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 $K = 2 \, N/cm$)

Medium

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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

Find the maximum amplitude (in $cm$) of the $SHM$ such that block $A$ will not slip on block $B$. Given: spring constant $K = 100 \ N/m$,mass of block $A$ $m_A = 0.25 \ kg$,mass of block $B$ $m_B = 1.25 \ kg$,and coefficient of friction between $A$ and $B$ is $\mu = 0.4$. Take $g = 10 \ m/s^2$.

$A$ spring has a certain mass suspended from it and its period for vertical oscillations is $T_1$. The spring is now cut into two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillations is now $T_2$. The ratio $T_1 / T_2$ is

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 $K = 2 \, N/cm$)

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