Two identical springs of spring constant $'2k'$ are attached to a block of mass $m$ and to fixed support (see figure). When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. The time period of oscillations of this sytem is ...... .
JEE MAIN 2021, Medium
Download our app for free and get started
For parallel combination $k _{ eq }= k _{1}+ k _{2}$
$k_{e q}=4 k$
$T =2 \pi \sqrt{\frac{ m }{ k _{ eq }}}$
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 block of mass $m$ attached to massless spring is performing oscillatory motion of amplitude $'A'$ on a frictionless horizontal plane. If half of the mass of the block breaks off when it is passing through its equilibrium point, the amplitude of oscillation for the remaining system become $fA.$ The value of $f$ isView Solution
- 2A particle of mass $2 \,kg$, executing $SHM$ has amplitude $20 \,cm$ and time period $1 \,s$. Its maximum speed is ......... $m / s$View Solution
- 3Consider two identical springs each of spring constant $k$ and negligible mass compared to the mass $M$ as shown. Fig. $1$ shows one of them and Fig. $2$ shows their series combination. The ratios of time period of oscillation of the two $SHM$ is $\frac{ T _{ b }}{ T _{ a }}=\sqrt{ x },$ where value of $x$ isView Solution
(Round off to the Nearest Integer)
- 4In simple harmonic motion, the total mechanical energy of given system is E. If mass of oscillating particle $P$ is doubled then the new energy of the system for same amplitude is:View Solution
- 5A particle executes $S.H.M.$ with a period of $6$ second and amplitude of $3\, cm$. Its maximum speed in $cm/sec$ isView Solution
- 6A pendulum clock that keeps correct time on the earth is taken to the moon it will run (it is given that $g_{Moon} = g_{Earth}/6$ )View Solution
- 7Two identical springs have the same force constant $73.5 \,Nm ^{-1}$. The elongation produced in each spring in three cases shown in Figure-$1$, Figure-$2$ and Figure-$3$ are $\left(g=9.8 \,ms ^{-2}\right)$View Solution
- 8If 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$View Solution
- 9Kinetic energy of a particle executing simple harmonic motion in straight line is $pv^2$ and potential energy is $qx^2$, where $v$ is speed at distance $x$ from the mean position. It time period is given by the expressionView Solution
- 10Two $SHM$ are represented by equations, $y_1 = 6\cos \left( {6\pi t + \frac{\pi }{6}} \right)\,,{y_2} = 3\left( {\sqrt 3 \sin 3\pi t + \cos 3\pi t} \right)$View Solution