(D) Let the bar be displaced downwards by a distance $x$. Since the bar remains horizontal,both springs stretch by the same amount $x$.The restoring f

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$2\pi \sqrt {\frac{{m}}{{4k}}} $

(D) Let the bar be displaced downwards by a distance $x$. Since the bar remains horizontal,both springs stretch by the same amount $x$.The restoring force in the first spring is $F_1 = kx$ and in the second spring is $F_2 = 3kx$.The total restoring force is $F = F_1 + F_2 = kx + 3kx = 4kx$.Comparing this with $F = k_{eq}x$,we get the equivalent spring constant $k_{eq} = 4k$.The time period of oscillation is given by $T = 2\pi \sqrt{\frac{m}{k_{eq}}}$.Substituting $k_{eq} = 4k$,we get $T = 2\pi \sqrt{\frac{m}{4k}}$.

Class 11 Physics Oscillations SHM of Spring Mass System

Difficult

$A$ bar of mass $m$ is suspended horizontally on two vertical springs of spring constant $k$ and $3k$. The bar bounces up and down while remaining horizontal. Find the time period of oscillation of the bar (Neglect mass of springs and friction everywhere).

A
$2\pi \sqrt {\frac{m}{k}} $
B
$2\pi \sqrt {\frac{m}{{3k}}} $
C
$\pi \sqrt {\frac{{2m}}{{3k}}} $
D
$2\pi \sqrt {\frac{{m}}{{4k}}} $

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Oscillations

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SHM of Spring Mass System

$A$ mass $M$ is suspended from a light spring. An additional mass $m$ added displaces the spring further by a distance $x$. Now the combined mass will oscillate on the spring with period

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Let $T_1$ and $T_2$ be the time periods of two springs $A$ and $B$ when a mass $m$ is suspended from them separately. Now both the springs are connected in parallel and the same mass $m$ is suspended with them. If $T$ is the new time period in this position,then:

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

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$A$ mass $m$ attached to a spring oscillates every $2 \, s$. If the mass is increased by $2 \, kg$,then the time period increases by $1 \, s$. The initial mass is ..... $kg$.

MediumAIIMS 2000

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Two bodies of masses $1\, kg$ and $4\, kg$ are connected to a vertical spring,as shown in the figure. The smaller mass executes simple harmonic motion of angular frequency $25\, rad/s$,and amplitude $1.6\, cm$ while the bigger mass remains stationary on the ground. The maximum force exerted by the system on the floor is ..... $N$ (take $g = 10\, m/s^2$).

DifficultJEE MAIN 2014

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$A$ bar of mass $m$ is suspended horizontally on two vertical springs of spring constant $k$ and $3k$. The bar bounces up and down while remaining horizontal. Find the time period of oscillation of the bar (Neglect mass of springs and friction everywhere).

Similar Questions

$A$ mass $M$ is suspended from a light spring. An additional mass $m$ added displaces the spring further by a distance $x$. Now the combined mass will oscillate on the spring with period

Let $T_1$ and $T_2$ be the time periods of two springs $A$ and $B$ when a mass $m$ is suspended from them separately. Now both the springs are connected in parallel and the same mass $m$ is suspended with them. If $T$ is the new time period in this position,then:

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