A particle performs $SHM$ with a period $T$ and amplitude $a.$ The mean velocity of the particle over the time interval during which it travels a distance $a/2$ from the extreme position is
Advanced
Download our app for free and get started
$x=A \cos \omega t \Rightarrow \frac{A}{2}=A \cos \omega t$
$\Rightarrow \quad \cos \omega t=\frac{1}{2}=\cos \frac{\pi}{3}$
$\frac{2 \pi}{T} t=\frac{\pi}{3}$
$\Rightarrow \quad t=\frac{T}{6}$
$v_{\mathrm{av}}=\frac{a / 2}{t}=\frac{a / 2}{T / 6}=\frac{3 a}{T}$
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
- 1A particle is executing simple harmonic motion with a period of $T$ seconds and amplitude a metre. The shortest time it takes to reach a point $\frac{a}{{\sqrt 2 }}\,m$ from its mean position in seconds isView Solution
- 2If the length of simple pendulum is increased by $300\%$, then the time period will be increased by ..... $\%$View Solution
- 3A block of mass $200\, g$ executing $SHM$ under the influence of a spring of spring constant $K=90\, N\,m^{-1}$ and a damping constant $b=40\, g\,s^{-1}$. The time elapsed for its amplitude to drop to half of its initial value is ...... $s$ (Given $ln\,\frac{1}{2} = -0.693$)View Solution
- 4View SolutionA hollow sphere is filled with water through a small hole in it. It is then hung by a long thread and made to oscillate. As the water slowly flows out of the hole at the bottom, the period of oscillation will
- 5Two simple harmonic motions of angular frequency $100$ and $1000\,\,rad\,s^{-1}$ have the same displacement amplitude. The ratio of their maximum acceleration isView Solution
- 6A light balloon filled with helium of density $\rho_{ He }$ is tied to a long light string of length $l$ and the string is attached to the ground. If the balloon is displaced slightly in the horizontal direction from the equilibrium and released. Then,View Solution
- 7A 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
- 8The length of the second pendulum on the surface of earth is $1\, m$. The length of seconds pendulum on the surface of moon, where g is 1/6th value of $g$ on the surface of earth, isView Solution
- 9A simple pendulum consisting of a light inextensible string of length $\ell$ attached to a heavy small bob of mass $m$ is at rest. The bob is imparted a horizontal impulsive force which gives it a speed of $\sqrt{4 g \ell}$. The speed of the bob at its highest point is ( $g$ is the accelaration due to gravity)View Solution
- 10A 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 tracesView Solution