The 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 by
AIEEE 2005, Easy
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
- 1View SolutionTo show that a simple pendulum executes simple harmonic motion, it is necessary to assume that
- 2Figure shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated on the figure. The simple harmonic motion of the $x-$ projection of the radius vector of the rotating particle $P$ isView Solution
- 3The potential energy of a particle of mass $4\,kg$ in motion along the $x$-axis is given by $U =4(1-\cos 4 x )\,J$. The time period of the particle for small oscillation $(\sin \theta \simeq \theta)$ is $\left(\frac{\pi}{ K }\right)\,s$. The value of $K$ is .......View Solution
- 4A uniform disc of mass $M$ and radius $R$ is suspended in vertical plane from a point on its periphery. Its time period of oscillation is ........View Solution
- 5View SolutionAn assembly of identical spring-mass systems is placed on a smooth horizontal surface as shown. At this instant, the springs are relaxed. The left mass is displaced to the/left and theiright mass is displaced to the right by same distance and released. The resulting collision is elastic. The time period of the oscillations of system is
- 6A simple pendulum is attached to the roof of a lift. If time period of oscillation, when the lift is stationary is $T$. Then frequency of oscillation, when the lift falls freely, will beView Solution
- 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
- 8View SolutionSelect wrong statement about simple,harmonic motion
- 9On a smooth inclined plane, a body of mass $M$ is attached between two springs. The other ends of the springs are fixed to firm supports. If each spring has force constant $K$, the period of oscillation of the body (assuming the springs as massless) isView Solution
- 10A body of mass $m $ is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass $m$ is slightly pulled down and released , it oscillates with a time period of $3\,s$ . When the mass $m$ is increased by $1\,kg$ , the time period of oscillations becomes $5\,s$ . The value of $m$ in $kg$ isView Solution