A mass $m$ is vertically suspended from a spring of negligible mass; the system oscillates with a frequency $n$. What will be the frequency of the system if a mass $4 m$ is suspended from the same spring
AIPMT 1998, Medium
Download our app for free and get started
(c)$n = \frac{1}{{2\pi }}\sqrt {\frac{k}{m}} $
$\Rightarrow n \propto \frac{1}{{\sqrt m }} $
$\Rightarrow \frac{{{n_1}}}{{{n_2}}} = \sqrt {\frac{{{m_2}}}{{{m_1}}}} $
$ \Rightarrow \frac{n}{{{n_2}}} = \sqrt {\frac{{4m}}{m}}$
$4\Rightarrow {n_2} = \frac{n}{2}$
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
- 1When an oscillator completes $100$ oscillations its amplitude reduced to $\frac{1}{3}$ of initial value. What will be its amplitude, when it completes $200$ oscillations?View Solution
- 2A particle is executing simple harmonic motion with an amplitude of $0.02$ metre and frequency $50\, Hz$. The maximum acceleration of the particle isView Solution
- 3The kinetic energy of $SHM$ is $1/n$ time its potential energy. If the amplitude of the $SHM$ be $A$, then what is the displacement of the particle?View Solution
- 4View SolutionIdentify the function which represents a periodic motion.
- 5A particle of mass $m$ performs $SHM$ along a straight line with frequency $f$ and amplitude $A.$View Solution
- 6A damped harmonic oscillator has a frequency of $5$ oscillations per second. The amplitude drops to half its value for every $10$ oscillations. The time it will take to drop to $\frac{1}{1000}$ of the original amplitude is close to .... $s$View Solution
- 7A pendulum is formed by pivoting a disc. What distance from center of mass, it should be pivoted for minimum time period while performing $SHM$ ?View Solution
- 8A spring mass system executes damped harmonic oscillations given by the equationView Solution
$y = A{e^{ - \frac{{bt}}{{2m}}}}\sin (\omega 't + \phi )$
where the symbols have their usual meanings. If a $2\ kg$ mass $(m)$ is attached to a spring of force constant $(K)$ $1250\ N/m$ , the period of the oscillation is $\left( {\pi /12} \right)s$ . The damping constant $‘b’$ has the value. ..... $kg/s$
- 9$Assertion :$ In $SHM$, acceleration is always directed towards the mean position.View Solution
$Reason :$ In $SHM$, the body has to stop momentary at the extreme position and move back to mean position. - 10The kinetic energy of a particle executing $S.H.M.$ is $16\, J$ when it is in its mean position. If the amplitude of oscillations is $25\, cm$ and the mass of the particle is $5.12\, kg$, the time period of its oscillation isView Solution