A particle performs simple harmonic motion with a period of $2$ second. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is $\frac{1}{ a } s .$ The value of $'a'$ to the nearest integer is.........
JEE MAIN 2021, Medium
Download our app for free and get started
$t =\frac{2}{12}=\frac{1}{6}$
$\therefore$ Correct answer $=6.00$
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
- 1An object of mass $0.2\, kg$ executes simple harmonic along $X-$ axis with frequency of $\frac{{25}}{\pi }Hz$. At the position $x = 0.04m$, the object has kinetic energy of $0.5 \,J$ and potential energy of $0.4\, J$ amplitude of oscillation in meter is equal toView Solution
- 2A body oscillates with a simple harmonic motion having amplitude $0.05\, m .$ At a certain instant, its displacement is $0.01\, m$ and acceleration is $1.0 \,m / s ^{2} .$ The period of oscillation isView Solution
- 3The piston in the cylinder head of locomotive has a stroke of $6\,m$ (which is twice the amplitude). If the piston executing simple harmonic motion with an angular frequency of $200\, rad\, min^{-1}$, its maximum speed is .... $ms^{-1}$View Solution
- 4A steady force of $120\ N$ is required to push a boat of mass $700\ kg$ through water at a constant speed of $1\ m/s$ . If the boat is fastened by a spring and held at $2\ m$ from the equilibrium position by a force of $450\ N$ , find the angular frequency of damped $SHM$ ..... $rad/s$View Solution
- 5A mass m oscillates with simple harmonic motion with frequency $f = \frac{\omega }{{2\pi }}$ and amplitude A on a spring with constant $K$ , thereforeView Solution
- 6The bob of simple pendulum having length $l$, is displaced from mean position to an angular position $\theta$ with respect to vertical. If it is released, then velocity of bob at lowest positionView Solution
- 7A particle executes linear simple harmonic motion with an amplitude of $2\, cm$. When the particle is at $1\, cm$ from the mean position the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds isView Solution
- 8The bob of a simple pendulum is displaced from its equilibrium position $O$ to a position $Q$ which is at height h above $O$ and the bob is then released. Assuming the mass of the bob to be $m$ and time period of oscillations to be $2.0\, sec$, the tension in the string when the bob passes through $O$ isView Solution
- 9A particle is executing the motion $x = A\cos (\omega \,t - \theta )$. The maximum velocity of the particle isView Solution
- 10Three masses $700g, 500g$, and $400g$ are suspended at the end of a spring a shown and are in equilibrium. When the $700g$ mass is removed, the system oscillates with a period of $3$ seconds, when the $500 \,gm$ mass is also removed, it will oscillate with a period of ...... $s$View Solution
