The displacement of a particle is given at time $t$, by:$x=A \sin (-2 \omega t)+B \sin ^2 \omega t \quad$ Then,
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
- 1The function $sin^2\,(\omega t)$ representsView Solution
- 2A block of mass $m$ rests on a platform. The platform is given up and down $SHM$ with an amplitude $d$ . What can be the maximum frequency so that the block never leaves the platformView Solution
- 3An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass $M$. The piston and the cylinder have equal cross sectional area $A$. When the piston is in equilibrium, the volume of the gas is $V_0$ and its pressure is $P_ 0$. The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequencyView Solution
- 4A particle starts with $S.H.M.$ from the mean position as shown in the figure. Its amplitude is $A$ and its time period is $T$. At one time, its speed is half that of the maximum speed. What is this displacement?View Solution
- 5A simple pendulum has time period $T_1$. The point of suspension is now moved upward according to equation $y = k{t^2}$ where $k = 1\,m/se{c^2}$. If new time period is $T_2$ then ratio $\frac{{T_1^2}}{{T_2^2}}$ will beView Solution
- 6A clock $S$ is based on oscillations of a spring and a clock $P$ is based on pendulum motion. Both clocks run at the same rate on earth. On a planet having same density as earth but twice the radius thenView Solution
- 7A 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 isView Solution
- 8Two $SHM$ are represented by equations, $y_1 = 6\cos \left( {6\pi t + \frac{\pi }{6}} \right)\,,{y_2} = 3\left( {\sqrt 3 \sin 3\pi t + \cos 3\pi t} \right)$View Solution
- 9A pendulum of length $2\,m$ lift at $P$. When it reaches $Q$, it losses $10\%$ of its total energy due to air resistance. The velocity at $Q$ is .... $m/sec$View Solution
- 10$Assertion :$ In simple harmonic motion, the velocity is maximum when the acceleration is minimum.View Solution
$Reason :$ Displacement and velocity of $S.H.M.$ differ in phase by $\frac{\pi }{2}$