The displacement of a body executing $SHM$ is given by $x = A \sin (2\pi t + \pi /3).$ The first time from $t = 0$ when the velocity is maximum is .... $\sec$
Medium
Download our app for free and get started
$x=A \sin \left(2 \pi t+\frac{\pi}{3}\right)$
Velocity is maximum at mean position i.e. $x=0$
$\Rightarrow \sin \left(2 \pi t+\frac{\pi}{3}\right)=0$
$\Rightarrow\left(2 \pi t+\frac{\pi}{3}\right)=0, \pi, 2 \pi, 3 \pi \dots$
if we take $\left(2 \pi t+\frac{\pi}{3}\right)=0,$ time will come negative which is not possible. So we take $\left(2 \pi t+\frac{\pi}{3}\right)=\pi$
$\Rightarrow t=\frac{1}{3} s=0.33 s$
for other solutions, we will get higher values of time. but since it is asking for the first time after $t=0,$ the required solution will be $t=0.33 s$
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
- 1The particle executing simple harmonic motion has a kinetic energy $K_0cos^2 \omega t$. The maximum values of the potential energy and the total energy are respectivelyView Solution
- 2A flat horizontal board moves up and down under $S.H.M.$ vertically with amplitude $A$. The shortest permissible time period of the vibration such that an object placed on the board may not lose contact with the board is ..........View Solution
- 3A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is $20\; m/s^2$ at a distance of $5\; m$ from the mean position. The time period of oscillation isView Solution
- 4A 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.View Solution
- 5View SolutionA simple pendulum is made of a body which is a hollow sphere containing mercury suspended by means of a wire. If a little mercury is drained off, the period of pendulum will
- 6A 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
- 7Which of the following expressions corresponds to simple harmonic motion along a straight line, where $x$ is the displacement and $a, b, c$ are positive constants?View Solution
- 8The drawing shows a top view of a frictionless horizontal surface, where there are two indentical springs with particles of mass $m_1$ and $m_2$ attached to them. Each spring has a spring constant of $1200\ N/m.$ The particles are pulled to the right and then released from the positions shown in the drawing. How much time passes before the particles are again side by side for the first time if $m_1 = 3.0\ kg$ and $m_2 = 27 \,kg \,?$View Solution
- 9A pendulum has time period $T$ in air. When it is made to oscillate in water, it acquired a time period $T' = \sqrt 2 T$. The density of the pendulum bob is equal to (density of water $= 1$)View Solution
- 10View SolutionWhich of the diagrams shown in figure represents variation of total mechanical energy of a pendulum oscillating in water as function of time ?