The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes of $4 \mathrm{~m}, 2 \mathrm{~ms}^{-1}$ and $16 \mathrm{~ms}^{-2}$ at a certain instant. The amplitude of the motion is $\sqrt{\mathrm{x}} \mathrm{m}$ where $\mathrm{x}$ is. . . . . . .
JEE MAIN 2024, Diffcult
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
- 1The acceleration of a particle performing S.H.M. is at a distance of $3\; cm$ from the mean position is $ 12\,cm/sec^2 $. Its time period is ..... $\sec$View Solution
- 2The displacements of two particles executing $S.H.M.$ on the same line are given. as $y_1=a \sin \left(\frac{\pi}{2} t+\phi\right)$ and $y_2=b \sin \left(\frac{2 \pi}{3} t+\phi\right)$. The phase difference between them at $t=1 \,s$ is .........View Solution
- 3$Assertion :$ In simple harmonic motion, the velocity is maximum when the acceleration is minimum.View Solution
$Reason :$ Displacement and velocity of $S.H.M.$ differ in phase by $\frac{\pi }{2}$ - 4An oscillator of mass $M$ is at rest in its equilibrium position in a potential $V\, = \,\frac{1}{2}\,k{(x - X)^2}.$ A particle of mass $m$ comes from right with speed $u$ and collides completely inelastically with $M$ and sticks to it . This process repeats every time the oscillator crosses its equilibrium position .The amplitude of oscillations after $13$ collisions is: $(M = 10,\, m = 5,\, u = 1,\, k = 1 ).$View Solution
- 5A particle is executing simple harmonic motion with a time period $T.$ At time $t = 0$, it is at its position of equilibrium. The kinetic energy-time graph of the particle will look likeView Solution
- 6The resultant of two rectangular simple harmonic motions of the same frequency and equal amplitudes but differing in phase by $\frac{\pi }{2}$ isView Solution
- 7The figure shows a graph between velocity and displacement (from mean position) of a particle performing $SHM\,:$View Solution
- 8The maximum velocity and the maximum acceleration of a body moving in a simple harmonic oscillator are $2\,m/s$ and $4\,m/{s^2}.$ Then angular velocity will be ..... $rad/sec$View Solution
- 9A 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
- 10When an oscillator completes $100$ oscillations its amplitude reduced to $\frac{1}{3}$ of initial value. What will be its amplitude, when it completes $200$ oscillations?View Solution