A particle of mass m is under the influence of a force $F$ which varies with the displacement $x$ according to the relation $F = - kx + {F_0}$ in which $k$ and ${F_0}$ are constants. The particle when disturbed will oscillate
i.e. the particle will oscillate about $x = \frac{{{F_0}}}{K}$
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A 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 .... $Hz$
A simple harmonic oscillator has an amplitude $A$ and time period $6 \pi$ second. Assuming the oscillation starts from its mean position, the time required by it to travel from $x=A$ to $x=\frac{\sqrt{3}}{2} A$ will be $\frac{\pi}{x}$ s, where $x=$__________.
A block of rectangular size of mass $m$ and area of cross-section $A$, floats in a liquid of density $\rho$. If we give a small vertical displacement from equilibrium, it undergoes $S H M$ with time period $T$, then
A block of mass $m$ hangs from three springs having same spring constant $k$. If the mass is slightly displaced downwards, the time period of oscillation will be
A particle is performing simple harmonic motion with amplitude A and angular velocity ${\omega }$. The ratio of maximum velocity to maximum acceleration is
A point mass is subjected to two simultaneous sinusoidal displacements in x-direction, $x_1(t)=A \sin \omega t $ and $ x_2(t)=A \sin \left(\omega t+\frac{2 \pi}{3}\right)$. Adding a third sinusoidal displacement $x_3(t)=B \sin (\omega t+\phi)$ brings the mass to a complete rest. The values of $B$ and $\phi$ are