As per given figures, two springs of spring constants $K$ and $2\,K$ are connected to mass $m$. If the period of oscillation in figure $(a)$ is $3 s$, then the period of oscillation in figure $(b)$ will be $\sqrt{ x }$ s. The value of $x$ is$.........$
JEE MAIN 2022, Medium
Download our app for free and get started
For figure $(a):$
$K _{\text {oq }}=\frac{ K \times 2 K }{ K +2 K }=\frac{2 K }{3}$
$T =2 \pi \sqrt{\frac{ m }{ K _{ eq }}}=2 \pi \sqrt{\frac{ m }{2 K / 3}}=2 \pi \sqrt{\frac{3 m }{2 K }}$
For figure $(b):$
$K _{ eq }=3 K , T ^{\prime}=2 \pi \sqrt{\frac{ m }{3 K }}$
$\frac{ T ^{\prime}}{ T }=\sqrt{\frac{ m \times 2 K }{3 K \times 3 m }}=\frac{\sqrt{2}}{3}$
$T ^{\prime}=\sqrt{2}$
$x =2$
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
- 1A particle executes simple harmonic motion and is located at $x = a, b$ and $c$ at times $t_0, 2t_0$ and $3t_0$ respectively. The frequency of the oscillation isView Solution
- 2A particle executing a simple harmonic motion of period $2\ s$ . When it is at its extreme displacement from its mean position, it receives an additional energy equal to what it had in its mean position. Due to this , in its subsequent motion,View Solution
- 3The equation of $S.H.M.$ is $y = a\sin (2\pi nt + \alpha )$, then its phase at time $t$ isView Solution
- 4Maximum amplitude(in $cm$) of $SHM$ so block A will not slip on block $B , K =100 N / m$View Solution
- 5A pendulum is executing simple harmonic motion and its maximum kinetic energy is $K_1$. If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the first case, its maximum kinetic energy is $K_2$ thenView Solution
- 6A particle is subjected to two mutually perpendicular simple harmonic motions such that its $x$ and $y$ coordinates are given by ?View Solution
$ x = 2 \sin \omega t \,;$ $ y = 2 \sin \left( {\omega t + \frac{\pi }{4}} \right)$
The path of the particle will be :
- 7Astone is swinging in a horizontal circle $0.8\, m$ in diameter at $30 \,rev / min.$ Adistant horizontal light beam causes a shadow of the stone to be formed on a nearly vertical wall. The amplitude and period of the simple harmonic motion for the shadow of the stone areView Solution
- 8A spring having a spring constant $‘K’$ is loaded with a mass $‘m’$. The spring is cut into two equal parts and one of these is loaded again with the same mass. The new spring constant isView Solution
- 9A lift is descending with acceleration $g/3$ . What will be the time period of a simple pendulum suspended from its ceiling if its time period in staionary life is $'T'$ ?View Solution
- 10The potential energy of a particle of mass $100 \,g$ moving along $x$-axis is given by $U=5 x(x-4)$, where $x$ is in metre. The period of oscillation is .................View Solution