A block is placed on a frictionless horizontal table. mass of block is m and springs are attached on

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13.Oscillations

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

${\left[ {\frac{{{K_1} + {K_2}}}{m}} \right]^{1/2}}$

${\left[ {\frac{{{K_1}{K_2}}}{{m({K_1} + {K_2})}}} \right]^{1/2}}$

${\left[ {\frac{{{K_1}{K_2}}}{{({K_1} - {K_2})m}}} \right]^{1/2}}$

${\left[ {\frac{{K_1^2 + K_2^2}}{{({K_1} + {K_2})m}}} \right]^{1/2}}$

Solution

(a)In this case springs are in parallel, so${k_{eq}} = {k_1} + {k_2}$
and $\omega = \sqrt {\frac{{{k_{eq}}}}{m}} = \sqrt {\frac{{{k_1} + {k_2}}}{m}} $

Standard 11

Physics

Maximum amplitude(in $cm$) of $SHM$ so block A will not slip on block $B , K =100 N / m$

hard

(AIIMS-2019)

Three masses $700g, 500g$ and $400g$ are suspended at the end of a spring a shown and are in equilibrium. When the $700g$ mass is removed, the system oscillates with a period of $3\,seconds$, when the $500g$ mass is also removed, it will oscillate with a period of …. $s$

medium

What is spring constant of spring ? Write its unit and dimensional formula.

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$A$ block of mass $M_1$ is hanged by a light spring of force constant $k$ to the top bar of a reverse Uframe of mass $M_2$ on the floor. The block is pooled down from its equilibrium position by $a$ distance $x$ and then released. Find the minimum value of $x$ such that the reverse $U$ -frame will leave the floor momentarily.

medium

Two springs, of force constants $k_1$ and $k_2$ are connected to a mass $m$ as shown. The frequency of oscillation of the mass is $f$ If both $k_1$ and $k_2$ are made four times their original values, the frequency of oscillation becomes

medium

(AIEEE-2007)

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

Solution

Similar Questions

Maximum amplitude(in $cm$) of $SHM$ so block A will not slip on block $B , K =100 N / m$

Three masses $700g, 500g$ and $400g$ are suspended at the end of a spring a shown and are in equilibrium. When the $700g$ mass is removed, the system oscillates with a period of $3\,seconds$, when the $500g$ mass is also removed, it will oscillate with a period of …. $s$

What is spring constant of spring ? Write its unit and dimensional formula.

Two springs, of force constants $k_1$ and $k_2$ are connected to a mass $m$ as shown. The frequency of oscillation of the mass is $f$ If both $k_1$ and $k_2$ are made four times their original values, the frequency of oscillation becomes

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