An assembly of identical spring-mass systems is placed on a smooth horizontal surface as shown. Initially the springs are relaxed. The left mass is displaced to the left while the right mass is displaced to the right and released. The resulting collision is elastic. The time period of the oscillations of the system is :-
A$2\pi \sqrt {\frac{{2M}}{k}} $
B$2\pi \sqrt {\frac{M}{{2k}}} $
C$2\pi \sqrt {\frac{M}{k}} $
D$\pi \sqrt {\frac{M}{k}} $
Medium
Download our app for free and get started
D$\pi \sqrt {\frac{M}{k}} $
d Each block completes half the oscillation
Download our app
and 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.*
A particle is performing simple harmonic motion
$(i)$ its velocity-displacement graph is parabolic in nature
$(ii)$ its velocity-time graph is sinusoidal in nature
$(iii)$ its velocity-acceleration graph is elliptical in nature
Correct answer is
A particle executing simple harmonic motion with amplitude of $0.1 \,m$. At a certain instant when its displacement is $0.02 \,m$, its acceleration is $0.5 \,m/s^2$. The maximum velocity of the particle is (in $m/s$)
The periodic time of a simple pendulum of length $1\, m $ and amplitude $2 \,cm $ is $5\, seconds$. If the amplitude is made $4\, cm$, its periodic time in seconds will be
A brass cube of side $a$ and density $\rho$ is floating in mercury of density $\sigma$. If the cube is displaced a bit vertically, it executes $S.H.M.$ Its time period will be
A mass m is suspended from a spring of length l and force constant $K$. The frequency of vibration of the mass is ${f_1}$. The spring is cut into two equal parts and the same mass is suspended from one of the parts. The new frequency of vibration of mass is ${f_2}$. Which of the following relations between the frequencies is correct
A block of mass m, attached to a spring of spring constant $k$, oscillates on a smooth horizontal table. The other end of the spring is fixed to a wall. The block has a speed $v$ when the spring is at its natural length. Before coming to an instantaneous rest, if the block moves a distance $x$ from the mean position, then
In an elevator, a spring clock of time period $T_S$ (mass attached to a spring) and a pendulum clock of time period $T_P$ are kept. If the elevator accelerates upwards