A particle has simple harmonic motion. The equation of its motion is $x = 5\sin \left( {4t - \frac{\pi }{6}} \right)$, where $x$ is its displacement. If the displacement of the particle is $3$ units, then it velocity is
Easy
Download our app for free and get started
(d) From the given equation, $a = 5$ and $\omega = 4$
$v = \omega \sqrt {{a^2} - {y^2}} = 4\sqrt {{{(5)}^2} - {{(3)}^2}} = 16$
$v = \omega \sqrt {{a^2} - {y^2}} = 4\sqrt {{{(5)}^2} - {{(3)}^2}} = 16$
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 spring whose unstretched length is $\ell $ has a force constant $k$. The spring is cut into two pieces of unstretched lengths $\ell_1$ and $\ell_2$ where, $\ell_1 = n\ell_2$ and $n$ is an integer. The ratio $k_1/k_2$ of the corresponding force constants, $k_1$ and $k_2$ will beView Solution
- 2A clock which keeps correct time at ${20^o}C$, is subjected to ${40^o}C$. If coefficient of linear expansion of the pendulum is $12 \times {10^{ - 6}}/^\circ C$. How much will it gain or loose in timeView Solution
- 3The angular velocities of three bodies in simple harmonic motion are ${\omega _1},\,{\omega _2},\,{\omega _3}$ with their respective amplitudes as ${A_1},\,{A_2},\,{A_3}$. If all the three bodies have same mass and velocity, thenView Solution
- 4An oscillator of mass $M$ is at rest in its equilibrium position in a potential $V\, = \,\frac{1}{2}\,k{(x - X)^2}.$ A particle of mass $m$ comes from right with speed $u$ and collides completely inelastically with $M$ and sticks to it . This process repeats every time the oscillator crosses its equilibrium position .The amplitude of oscillations after $13$ collisions is: $(M = 10,\, m = 5,\, u = 1,\, k = 1 ).$View Solution
- 5A ring is hung on a nail. It can oscillate, without slipping or sliding $(i)$ in its plane with a time period $T_{1}$ and, $(ii)$ back and forth in a direction perpendicular to its plane, with a period $T _{2}$. the ratio $\frac{ T _{1}}{ T _{2}}$ will beView Solution
- 6A 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
- 7Two simple harmonic motions are represented by the equations ${y_1} = 0.1\sin \left( {100\pi t + \frac{\pi }{3}} \right)$ and ${y_2} = 0.1\cos \pi t.$ The phase difference of the velocity of particle $1$ with respect to the velocity of particle $2$ isView Solution
- 8Match $List - I$ with $List - II$View Solution
Choose the correct answer from the options given below
- 9There is a simple pendulum hanging from the ceiling of a lift. When the lift is stand still, the time period of the pendulum is $T$. If the resultant acceleration becomes $g/4,$ then the new time period of the pendulum isView Solution
- 10The angular velocity and the amplitude of a simple pendulum is $'\omega '$ and $'A'$ respectively. At a displacement $x$ from the mean position its kinetic energy is $'T'$ and potnetial energy is $'V'$. Then the ratio $\frac{V}{T}$ isView Solution