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 : $\pi=3.14$ )
JEE MAIN 2022, Medium
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 executes $S.H.M.$ and its position varies with time as $x=A$ sin $\omega t$. Its average speed during its motion from mean position to mid-point of mean and extreme position isView Solution
- 2A particle executing simple harmonic motion along $Y- $axis has its motion described by the equation $y = A\sin (\omega \,t) + B$. The amplitude of the simple harmonic motion isView Solution
- 3Two 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?View Solution
- 4In the given figure, a mass $M$ is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is $k$. The mass oscillates on a frictionless surface with time period $T$ and amplitude $A$. When the mass is in equilibrium position, as shown in the figure, another mass $m$ is gently fixed upon it. The new amplitude of oscillation will beView Solution
- 5The general displacement of a simple harmonic oscillator is $x = A \sin \omega t$. Let $T$ be its time period. The slope of its potential energy (U) - time (t) curve will be maximum when $t=\frac{T}{\beta}$. The value of $\beta$ is $.........$View Solution
- 6Two simple pendulums of lengths $1.44 \,m$ and $1\, m$ start swinging together. After how many vibrations will they again start swinging togetherView Solution
- 7A simple pendulum is executing simple harmonic motion with a time period $T$. If the length of the pendulum is increased by $21\%$, the percentage increase in the time period of the pendulum of increased length is ..... $\%$View Solution
- 8A heavy small-sized sphere is suspended by a string of length $l$. The sphere rotates uniformly in a horizontal circle with the string making an angle $\theta $ with the vertical. Then the time period of this conical pendulum isView Solution
- 9View SolutionResonance is an example of
- 10View SolutionIn simple harmonic motion, the ratio of acceleration of the particle to its displacement at any time is a measure of