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Two springs with spring constants ${K_1} = 1500\,N/m$ and ${K_2} = 3000\,N/m$ are stretched by the same force. The ratio of potential energy stored in spring will be
When a mass $M$ is attached to the spring of force constant $k$, then the spring stretches by $l$. If the mass oscillates with amplitude $l$, what will be maximum potential energy stored in the spring
As per given figures, two springs of spring constants $K$ and $2\,K$ are connected to mass $m$. If the period of oscillation in figure $(a)$ is $3 s$, then the period of oscillation in figure $(b)$ will be $\sqrt{ x }$ s. The value of $x$ is$.........$
A block of mass $0.1\, kg$ is connected to an elastic spring of spring constant $640\, Nm^{-1}$ and oscillates in a damping medium of damping constant $10^{-2}\, kg\,s^{-1}$ . The system dissipates its energy gradually. The time taken for its mechanical energy of vibration to drop to half of its initial value, is closest to ..... $s$
A book is resting on a shelf that is undergoing vertical simple harmonic oscillations with an amplitude of $2.5 \,cm$. What is the minimum frequency of oscillation of the shelf for .......... $Hz$ the book will lose contact with the shelf? (Assume that, $g=10 \,ms ^{-2}$ )
A particle is executing $S.H.M.$ and its velocity $v$ is related to its position $(x)$ as $v^2+a x^2=b$, where $a$ and $b$ are positive constants. The frequency of oscillation of particle is ..........
The displacement of a particle varies according to the relation $x = 3 \sin 100 \, t + 8 \cos ^2 50\,t $. Which of the following is/are correct about this motion .
A particle performs simple harmonic motion with amplitude A. Its speed is increased to three times at an instant when its displacement is $\frac{2 \mathrm{~A}}{3}$. The new amplitude of motion is $\frac{\mathrm{nA}}{3}$. The value of $\mathrm{n}$ is____.