The plot of velocity $(v)$ versus displacement $(x)$ of a particle executing simple harmonic motion is shown in figure. The time period of oscillation of particle is .........
A$\frac{\pi}{2} s$
B$\pi s$
C$2 \pi s$
D$3 \pi s$
Medium
Download our app for free and get started
A$\frac{\pi}{2} s$
a (a)
$A=10 \,cm \quad A \omega=0.4 \,m / s$
$=0.1 \,m$
$\therefore \omega =4 \,rad / s$
$T=\frac{2 \pi}{4}=\frac{\pi}{2} s$
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 of $2.0\, kg$ is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible. When pressed slightly and released the mass executes a simple harmonic motion. The spring constant is $200\, N/m.$ What should be the minimum amplitude of the motion so that the mass gets detached from the pan (take $g = 10 m/s^2$).
Two bodies performing $SHM$ have same amplitude and frequency. Their phases at a certain instant are as shown in the figure. The phase difference between them is
In forced oscillation of a particle the amplitude is maximum for a frequency $\omega_{1}$ of the force, while the energy is maximum for a frequency $\omega_{2}$ of the force, then
The equation of a particle executing simple harmonic motion is given by $x =\sin \pi\left( t +\frac{1}{3}\right) m$. At $t =1 \,s$, the speed of particle will be .......... $cm s ^{-1}$ (Given : $\pi=3.14$ )
$Assertion :$ In $SHM$, acceleration is always directed towards the mean position.
$Reason :$ In $SHM$, the body has to stop momentary at the extreme position and move back to mean position.
A particle is placed at the lowest point of a smooth wire frame in the shape of a parabola, lying in the vertical $xy-$ plane having equation $x^2 = 5y$ $(x, y$ are in meter). After slight displacement, the particle is set free. Find angular frequency of oscillation.....$rad/s$ (in $rad/sec$ ) (take $g = 10\ m/s^2$ )