A mass $\mathrm{m}$ is suspended from a spring of negligible mass and the system oscillates with a frequency $f_1$. The frequency of oscillations if a mass $9 \mathrm{~m}$ is suspended from the same spring is $f_2$. The value of $\frac{f_1}{f_{.2}}$ is_____________.
JEE MAIN 2024, Diffcult
Download our app for free and get started
$\mathrm{f}_1=\frac{1}{2 \pi} \sqrt{\frac{\mathrm{k}}{\mathrm{m}}}$
$\mathrm{f}_2=\frac{1}{2 \pi} \sqrt{\frac{\mathrm{k}}{9 \mathrm{~m}}}$
$\frac{\mathrm{f}_1}{\mathrm{f}_2}=\sqrt{\frac{9}{1}}=\frac{3}{1}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1Time period of a simple pendulum is $T$. The angular displacement for amplitude is $\beta$. How much time the bob of pendulum will take to move from equilibrium position $O$ to $A$, making an angle $\alpha$ at the supportView Solution
- 2View SolutionThe diagram shows two oscillations. What is the phase difference between the oscillations?
- 3A simple pendulum is suspended in a car. The car starts moving on a horizontal road according to equation $x\, = \,\frac{g}{2}\,\sqrt 3 {t^2}$. Find the time period of oscillation of the pendulum.View Solution
- 4A book is resting on a shelf that is undergoing vertical simple harmonic oscillations with an amplitude of $2.5 \,cm$. What is the minimum frequency of oscillation of the shelf for .......... $Hz$ the book will lose contact with the shelf? (Assume that, $g=10 \,ms ^{-2}$ )View Solution
- 5The total mechanical energy of a particle in $SHM$ isView Solution
- 6A mass at the end of a spring executes harmonic motion about an equilibrium position with an amplitude $A.$ Its speed as it passes through the equilibrium position is $V.$ If extended $2A$ and released, the speed of the mass passing through the equilibrium position will beView Solution
- 7When the displacement of a simple harmonic oscillator is one third of its amplitude, the ratio of total energy to the kinetic energy is $\frac{x}{8}$, where $x=$_____________.View Solution
- 8Two blocks $A$ and $B$ each of mass m are connected by a massless spring of natural length L and spring constant $K$. The blocks are initially resting on a smooth horizontal floor with the spring at its natural length as shown in figure. A third identical block $C$ also of mass $m$ moves on the floor with a speed $v$ along the line joining $A$ and $B$ and collides with $A$. ThenView Solution
- 9View SolutionIn a simple harmonic oscillator, at the mean position
- 10View SolutionWhich of the following function represents a simple harmonic oscillation