A particle moves on $x-$ axis according to the equation $x = x_0\,\,sin^2\,\omega t,$ the motion is simple harmonic
Medium
Download our app for free and get started
$\mathrm{x}=\mathrm{x}_{0} \sin ^{2} \omega \mathrm{t}$
$x=x_{0}\left[\frac{1-\cos 2 \omega t}{2}\right]=\frac{x_{0}}{2}-\frac{x_{0} \cos 2 \omega t}{2}$
Angular Frequency $=2 \omega$
$\frac{2 \pi}{\mathrm{T}}=2 \omega$
$\mathrm{T}=\frac{\pi}{\omega}$
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 displacement of a particle executing SHM is given by $x=10 \sin \left(\omega t+\frac{\pi}{3}\right) \mathrm{m}$. The time period of motion is $3.14 \mathrm{~s}$. The velocity of the particle at $\mathrm{t}=0$is_________. $\mathrm{m} / \mathrm{s}$.View Solution
- 2The equation of motion of a particle is $\frac{{{d^2}y}}{{d{t^2}}} + Ky = 0$, where $K$ is positive constant. The time period of the motion is given byView Solution
- 3The equation of a simple harmonic motion is $X = 0.34\cos (3000t + 0.74)$ where $X$ and $t$ are in $mm$ and $sec$. The frequency of motion isView Solution
- 4A linear harmonic oscillator of force constant $2 \times 10^6\,Nm^{-1}$ and amplitude $0.01\, m$ has a total mechanical energy of $160\, J.$ ItsView Solution
- 5The time period of simple harmonic motion of mass $\mathrm{M}$ in the given figure is $\pi \sqrt{\frac{\alpha M}{5 K}}$, where the value of $\alpha$ is____.View Solution
- 6View SolutionTime period of a simple pendulum will be double, if we
- 7Consider two identical cylinders [each of mass $m$ density $\rho _0$ horizontal cross-section area $s$] in equilibrium, partially submerged in two containers filled with liquids of densities $\rho_1$ and $\rho_2$ as shown in figure. Find the period of small oscillations of this system about its equilibrium. Neglect the changes in the level of liquids in the containers. Neglect mass of the strings. acceleration due to gravity is $g$ . ($v$ is volume of each block)View Solution
- 8A particle is executing $S.H.M.$ with time period $T^{\prime}$. If time period of its total mechanical energy is $T$ then $\frac{T^{\prime}}{T}$ is ........View Solution
- 9A wooden cube (density of wood $'d'$ ) of side $'l'$ floats in a liquid of density $'\rho '$ with its upper and lower surfaces horizontal. If the cube is pushed slightly down and released, it performs simple harmonic motion of period $'T'$. Then, $'T'$ is equal toView Solution
- 10A vibratory motion is represented by $x = 2A\,\cos \omega t + A\,\cos \,\left( {\omega t + \frac{\pi }{2}} \right) + A\,\cos \,\left( {\omega t + \pi } \right)$ $ + \frac{A}{2}\,\cos \left( {\omega t + \frac{{3\pi }}{2}} \right)$. The resultant amplitude of the motion isView Solution