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A mass $m$ is suspended by means of two coiled spring which have the same length in unstretched condition as in figure. Their force constant are $k_1$ and $k_2$ respectively. When set into vertical vibrations, the period will be
The particle executing simple harmonic motion has a kinetic energy $K_0cos^2 \omega t$. The maximum values of the potential energy and the total energy are respectively
$Assertion :$ In simple harmonic motion, the velocity is maximum when the acceleration is minimum.
$Reason :$ Displacement and velocity of $S.H.M.$ differ in phase by $\frac{\pi }{2}$
A simple pendulum is set up in a trolley which moves to the right with an acceleration a on a horizontal plane. Then the thread of the pendulum in the mean position makes an angle $\theta $ with the vertical
Two particles are performing simple harmonic motion in a straight line about the same equilibrium point. The amplitude and time period for both particles are same and equal to $A$ and $T,$ respectively. At time $t=0$ one particle has displacement $A$ while the other one has displacement $\frac {-A}{2}$ and they are moving towards each other. If they cross each other at time $t,$ then $t$ is
A man weighing $60\, kg$ stands on the horizontal platform of a spring balance. The platform starts executing simple harmonic motion of amplitude $0.1\, m$ and frequency $\frac{2}{\pi }Hz$. Which of the following statement is correct
A body is executing $S.H.M.$ When its displacement from the mean position is $4\, cm$ and $5\, cm$, the corresponding velocity of the body is $10 \,cm/sec$ and $8\, cm/sec$. Then the time period of the body is