A 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 is
A$0.1 \,s$
B$0.2 \,s$
C$\frac{\pi}{10}\, s$
D$\frac{\pi}{5}\, s$
AIIMS 2019, Medium
Download our app for free and get started
D$\frac{\pi}{5}\, s$
d The angular frequency is given as,
$| a |=\omega^{2} y$
$1=\omega^{2} \times 0.01$
$\omega^{2}=\frac{1}{0.01}=100$
$\omega=10 rad / s$
The time period comes out to be,
$T =\frac{2 \pi}{\omega}$
$T =\frac{2 \pi}{10 rad / s }=\frac{\pi}{5} sec$
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 executes $SHM$ on a straight line path. The amplitude of oscillation is $2\, cm.$ When the displacement of the particle from the mean position is $1\, cm,$ the numerical value of magnitude of acceleration is equal to the numerical value of magnitude of velocity. The frequency of $SHM$ (in $second^{-1}$) is :
A $1.00 \times {10^{ - 20}}kg$ particle is vibrating with simple harmonic motion with a period of $1.00 \times {10^{ - 5}}sec$ and a maximum speed of $1.00 \times {10^3}m/s$. The maximum displacement of the particle is
A pendulum with time period of $1\, s$ is losing energy due to damping. At certain time its energy is $45\, J$. If after completing $15\,oscillations$ , its energy has become $15\, J$, its damping constant (in $s^{-1}$ ) is
A block of mass $m$ hangs from three springs having same spring constant $k$. If the mass is slightly displaced downwards, the time period of oscillation will be
A simple pendulum of length $1\, m$ is oscillating with an angular frequency $10\, rad/s$. The support of the pendulum starts oscillating up and down with a small angular frequency of $1\, rad/s$ and an amplitude of $10^{-2}\, m$. The relative change in the angular frequency of the pendulum is best given by
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 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 ..... $\sec$