(C) The frequency of a spring-mass system is given by $f = \frac{1}{2 \pi} \sqrt{\frac{k}{m}}$.For the first case: $1 = \frac{1}{2 \pi} \sqrt{\frac{k}

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(C) The frequency of a spring-mass system is given by $f = \frac{1}{2 \pi} \sqrt{\frac{k}{m}}$.For the first case: $1 = \frac{1}{2 \pi} \sqrt{\frac{k}{1}}$,which implies $k = 4 \pi^2 \, N/m$.In the second case,two identical springs are connected in parallel,so the equivalent spring constant is $k_{eq} = k + k = 2k = 2(4 \pi^2) = 8 \pi^2 \, N/m$.The new mass is $M = 8 \, kg$.The new frequency $f'$ is given by:$f' = \frac{1}{2 \pi} \sqrt{\frac{k_{eq}}{M}} = \frac{1}{2 \pi} \sqrt{\frac{8 \pi^2}{8}} = \frac{1}{2 \pi} \sqrt{\pi^2} = \frac{\pi}{2 \pi} = 0.5 \, Hz$.

Class 11 Physics Oscillations SHM of Spring Mass System

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$A$ $1 \, kg$ block attached to a spring vibrates with a frequency of $1 \, Hz$ on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an $8 \, kg$ block placed on the same table. The frequency of vibration of the $8 \, kg$ block is ..... $Hz$.

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Two bodies $A$ and $B$ of equal mass are suspended from two separate massless springs of spring constants $K_1$ and $K_2$ respectively. The two bodies oscillate vertically such that their maximum velocities are equal. The ratio of the amplitude of $B$ to that of $A$ is

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If a body of mass $0.98\, kg$ is made to oscillate on a spring of force constant $4.84\, N/m$,the angular frequency of the body is ..... $rad/s$. (in $.22$)

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$A$ spring with a force constant $180 \text{ N/m}$ is loaded with a mass $0.2 \text{ kg}$. The amplitude of oscillations is $4 \text{ cm}$. When the mass comes to the equilibrium position, its velocity is: (in $\text{ m/s}$)

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The springs shown in the figure are identical,each having a spring constant $K$. When mass $A = 4\, kg$ is attached,the elongation of the spring is $1\, cm$. If mass $B = 6\, kg$ is attached to the system of two springs in series as shown,the total elongation produced is ..... $cm$.

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$A$ $1 \, kg$ block attached to a spring vibrates with a frequency of $1 \, Hz$ on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an $8 \, kg$ block placed on the same table. The frequency of vibration of the $8 \, kg$ block is ..... $Hz$.

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Two bodies $A$ and $B$ of equal mass are suspended from two separate massless springs of spring constants $K_1$ and $K_2$ respectively. The two bodies oscillate vertically such that their maximum velocities are equal. The ratio of the amplitude of $B$ to that of $A$ is

$A$ mass $M$ is suspended from a light spring. An additional mass $M_1$ added extends the spring further by a distance $x$. Now the combined mass will oscillate on the spring with period $T=$

If a body of mass $0.98\, kg$ is made to oscillate on a spring of force constant $4.84\, N/m$,the angular frequency of the body is ..... $rad/s$. (in $.22$)

$A$ spring with a force constant $180 \text{ N/m}$ is loaded with a mass $0.2 \text{ kg}$. The amplitude of oscillations is $4 \text{ cm}$. When the mass comes to the equilibrium position, its velocity is: (in $\text{ m/s}$)

The springs shown in the figure are identical,each having a spring constant $K$. When mass $A = 4\, kg$ is attached,the elongation of the spring is $1\, cm$. If mass $B = 6\, kg$ is attached to the system of two springs in series as shown,the total elongation produced is ..... $cm$.

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