A particle moves such that its acceleration $a$ is given by $a = - bx$, where $x$ is the displacement from equilibrium position and b is a constant. The period of oscillation is
A$2\pi \sqrt b $
B$\frac{{2\pi }}{{\sqrt b }}$
C$\frac{{2\pi }}{b}$
D$2\sqrt {\frac{\pi }{b}} $
Easy
Download our app for free and get started
B$\frac{{2\pi }}{{\sqrt b }}$
b (b) In the given case, $\frac{{Displacement}}{{Acceleration}} = \frac{1}{b}$
ime period $T = 2\pi \sqrt {\frac{{Displacement}}{{Acceleration}}} = \frac{{2\pi }}{{\sqrt b }}$
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 mass $m = 1.0\,kg$ is put on a flat pan attached to a vertical spring fixed on the ground. The mass of the spring and the pan is negligible. When pressed slightly and released, the mass executes simple harmonic motion. The spring constant is $500\,N/m.$ What is the amplitude $A$ of the motion, so that the mass $m$ tends to get detached from the pan ? (Take $g = 10\,m/s^2$ ). The spring is stiff enough so that it does not get distorted during the motion.
A system of two identical rods ($L-$ shaped) of mass $m$ and length $l$ are resting on a peg $P$ as shown in the figure. If the system is displaced in its plane by a small angle $\theta ,$ find the period of oscillations :
A mass $m$ attached to a spring oscillates every $2\, sec$. If the mass is increased by $2 \,kg$, then time-period increases by $1\, sec$. The initial mass is ..... $kg$
A particle executes harmonic motion with an angular velocity and maximum acceleration of $3.5\, rad/sec$ and $ 7.5\, m/s^2$ respectively. The amplitude of oscillation is .... $m$
A simple pendulum of frequency $f$ has a metal bob. If bob is charged negatively and is allowed to oscillate with large positive charged plate under it, frequency will be
A particle moves in $xy$ plane according to the law $x = a \sin \omega t$ and $y = a(1-\cos \omega t)$ where $a$ and $\omega$ are constants. The particle traces
$Assertion :$ For a particle performing $SHM$, its speed decreases as it goes away from the mean position.
$Reason :$ In $SHM$, the acceleration is always opposite to the velocity of the particle.
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 light pointer fixed to one prong of a tuning fork touches a vertical plate. The fork is set vibrating and the plate is allowed to fall freely. If eight oscillations are counted when the plate falls through $10 cm$, the frequency of the tuning fork is .... $Hz$
A particle moves with simple harmonic motion in a straight line. In first $\tau \,s,$ after starting from rest it travels a distance $a,$ and in next $\tau \,s$ it travels $2a,$ in same direction, then