(B) The time period of a spring-block system is given by $T = 2 \pi \sqrt{\frac{m}{k}}$.For a given spring,$T \propto \sqrt{m}$.Therefore,$\frac{T_{1}

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(B) The time period of a spring-block system is given by $T = 2 \pi \sqrt{\frac{m}{k}}$.For a given spring,$T \propto \sqrt{m}$.Therefore,$\frac{T_{1}}{T_{2}} = \sqrt{\frac{m_{1}}{m_{2}}}$.Here,$T_{1} = 3 \ s$,$m_{1} = m$,$T_{2} = 5 \ s$,and $m_{2} = m + 1$.Substituting the values: $\frac{3}{5} = \sqrt{\frac{m}{m+1}}$.Squaring both sides: $\frac{9}{25} = \frac{m}{m+1}$.Cross-multiplying: $9(m + 1) = 25m \Rightarrow 9m + 9 = 25m$.$16m = 9 \Rightarrow m = \frac{9}{16} \ kg$.

Class 11 Physics Oscillations SHM of Spring Mass System

Medium

$A$ body of mass $m$ is attached to the lower end of a spring whose upper end is fixed. The mass of the spring is negligible. When the mass $m$ is pulled down slightly and released,it oscillates with a time period of $3 \ s$. When the mass $m$ is increased by $1 \ kg$,the time period of oscillation becomes $5 \ s$. What is the value of $m$ in $kg$?

NEET 2016 All NEET

A
$\frac{16}{9}$
B
$\frac{9}{16}$
C
$\frac{3}{4}$
D
$\frac{4}{3}$

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SHM of Spring Mass System

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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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$A$ mass suspended from a vertical spring performs $S.H.M.$ with a period of $T = 0.1 \ s$. The spring is unstretched at the highest point of its motion. What is the maximum speed of the mass? (Take gravitational acceleration $g = 10 \ m/s^2$)

MediumMHT CET 2025

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$A$ particle of mass $200 \,g$ executes $S.H.M.$ The restoring force is provided by a spring of force constant $80 \,N/m$. The time period of oscillations is .... $s$.

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When a body of mass $m$ is suspended from a spiral spring,the spring stretches by a distance of $20\, cm$. If the spring is further stretched by a small distance and released,what is the period of oscillation (in $, s$)?

Easy

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$A$ stiff spring having spring constant $k = 400 \text{ N/m}$ is attached to the floor vertically. $A$ mass $m = 10 \text{ kg}$ is placed on top of the spring. The block oscillates if it is pressed downward and released. Find the extension in the spring at which the block loses contact with the spring. (Take $g = 10 \text{ m/s}^2$) (in $\text{ cm}$)

MediumTS EAMCET 2020

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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 $\text{ m/s}$)

$A$ mass suspended from a vertical spring performs $S.H.M.$ with a period of $T = 0.1 \ s$. The spring is unstretched at the highest point of its motion. What is the maximum speed of the mass? (Take gravitational acceleration $g = 10 \ m/s^2$)

$A$ particle of mass $200 \,g$ executes $S.H.M.$ The restoring force is provided by a spring of force constant $80 \,N/m$. The time period of oscillations is .... $s$.

When a body of mass $m$ is suspended from a spiral spring,the spring stretches by a distance of $20\, cm$. If the spring is further stretched by a small distance and released,what is the period of oscillation (in $, s$)?

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