A plank with a small block on top of it is under going vertical $SHM$ . Its period is $2\ sec$ . The minimum amplitude at which the block will separate from plank is
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Two simple harmonic motions are represented by equations ${y_1} = 4\,\sin \,\left( {10t + \phi } \right)$ and ${y_2} = 5\,\cos \,10\,t$ What is the phase difference between their velocities?
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 staements is correct
A mass $m =100\, gms$ is attached at the end of a light spring which oscillates on a frictionless horizontal table with an amplitude equal to $0.16$ metre and time period equal to $2 \,sec$. Initially the mass is released from rest at $t = 0$ and displacement $x = - 0.16$ metre. The expression for the displacement of the mass at any time $t$ is
A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is $4 \mathrm{~m}$, then the time period of small oscillations will be ____ $s$. $\left[\right.$ take $\left.\mathrm{g}=\pi^2 \mathrm{~ms}^{-2}\right]$
Two particles $P$ and $Q$ describe simple harmonic motions of same period, same amplitude, along the same line about the same equilibrium position $O.$ When $P$ and $Q$ are on opposite sides of $O$ at the same distance from $O$ they have the same speed of $1.2 \,m/s$ in the same direction, when their displacements are the same they have the same speed of $1.6\, m/s$ in opposite directions. The maximum velocity in $m/s$ of either particle is
Two independent harmonic oscillators of equal mass are oscillating about the origin with angular frequencies $\omega_1$ and $\omega_2$ and have total energies $E_1$ and $E_2$, respectively. The variations of their momenta $p$ with positions $x$ are shown in the figures. If $\frac{a}{b}= n ^2$ and $\frac{ a }{ R }= n$, then the correct equation$(s)$ is(are) $Image$
A particle executes $S.H.M$ between $x =\, -A$ to $x =\, +A$ . The time taken for it in going from $0$ to $A/2$ is $T_1$ and from $A/2$ to $A$ is $T_2$. Then
A mass $0.9\,kg$, attached to a horizontal spring, executes $SHM$ with an amplitude $A _{1}$. When this mass passes through its mean position, then a smaller mass of $124\,g$ is placed over it and both masses move together with amplitude $A _{2}$. If the ratio $\frac{ A _{1}}{ A _{2}}$ is $\frac{\alpha}{\alpha-1}$, then the value of $\alpha$ will be$......$