When the potential energy of a particle executing simple harmonic motion is one-fourth of its maximum value during the oscillation, the displacement of the particle from the equilibrium position in terms of its amplitude $a$ is
AIPMT 1993, 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 light pointer fixed to one prong of a tuning fork touches a vertical plate. The fork is set vibrating and the plate is allowed to fall freely. If eight oscillations are counted when the plate falls through $10 cm$, the frequency of the tuning fork is .... $Hz$View Solution
- 2Two springs of force constants $300\, N/m$ (Spring $A$) and $400\, N/m$ (Spring $B$) are joined together in series . The combination is compressed by $8.75\, cm$. The ratio of energy stored in $A$ and $B$ is $\frac{{{E_A}}}{{{E_B}}}$. Then $\frac{{{E_A}}}{{{E_B}}}$ is equal toView Solution
- 3A uniform rod of length $L$ and mass $M$ is pivoted at the centre. Its two ends are attached to two springs of equal spring constants $k$. The springs are fixed to rigid supports as shown in the figure, and the rod is free to oscillate in the horizontal plane. The rod is gently pushed through a small angle $\theta$ in one direction and released. The frequency of oscillation isView Solution
- 4A plank with a small block on top of it is under going vertical $SHM.$ Its period is $2\, sec.$ The minimum amplitude at which the block will separate from plank is :View Solution
- 5An object of mass $0.2\ kg$ executes simple harmonic along $X-$ axis with frequency of $\frac{{25}}{\pi } Hz$ . At the position $x$ = $0.04\ m$ , the object has kinetic energy of $0.5\ J$ and potential energy of $0.4\ J$ amplitude of oscillation in meter is equal toView Solution
- 6The position co-ordinates of a particle moving in a $3-D$ coordinates system is given by $x = a\,cos\,\omega t$ , $y = a\,sin\,\omega t$ and $z = a\omega t$ The speed of the particle isView Solution
- 7The drawing shows a top view of a frictionless horizontal surface, where there are two indentical springs with particles of mass $m_1$ and $m_2$ attached to them. Each spring has a spring constant of $1200\ N/m.$ The particles are pulled to the right and then released from the positions shown in the drawing. How much time passes before the particles are again side by side for the first time if $m_1 = 3.0\ kg$ and $m_2 = 27 \,kg \,?$View Solution
- 8View SolutionA particle is moving with constant angular velocity along the circumference of a circle. Which of the following statements is true
- 9A large horizontal surface moves up and down in $S.H.M.$ with an amplitude of $1\, cm$. If a mass of $10\, kg$ (which is placed on the surface is to remain continuously in contact with it, the maximum frequency of $S.H.M.$ will be .... $Hz$View Solution
- 10The maximum speed of a particle executing $S.H.M.$ is $1\,m/s$ and its maximum acceleration is $1.57\,m/se{c^2}$. The time period of the particle will be .... $\sec$View Solution