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The variations of potential energy $(U)$ with position $x$ for three simple harmonic oscillators $A, B$ and $C$ are shown in figure. The oscillators have same mass. The time period of oscillation is greatest for
The force-deformation equation for a nonlinear spring fixed at one end is $F =4x^{1/ 2}$ , where $F$ is the force (expressed in newtons) applied at the other end and $x$ is the deformation expressed in meters
A body is executing simple harmonic motion of amplitude $a$ and period $T$ about the equilibrium position $x=0$. Large numbers of snapshots are taken at random of this body in motion. The probability of the body being found in a very small interval $x$ to $x+|d x|$ is highest at
Two particles are in $SHM$ on same straight line with amplitude $A$ and $2A$ and with same angular frequency $\omega .$ It is observed that when first particle is at a distance $A/\sqrt{2}$ from origin and going toward mean position, other particle is at extreme position on other side of mean position. Find phase difference between the two particles
Two waves executing simple harmonic motion travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the $\sqrt{3}$ times of amplitude of individual motions. The phase difference between the two motions is $.....(degree)$
A particle is performing simple harmonic motion
$(i)$ its velocity-displacement graph is parabolic in nature
$(ii)$ its velocity-time graph is sinusoidal in nature
$(iii)$ its velocity-acceleration graph is elliptical in nature
Correct answer is
The amplitude of a particle executing $SHM$ is $3\,cm$. The displacement at which its kinetic energy will be $25 \%$ more than the potential energy is: $.............cm$.
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, $g=10 \,ms ^{-2}$ )