When a mass $m$ is attached to a spring, it normally extends by $0.2\, m$. The mass $m$ is given a slight addition extension and released, then its time period will be
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A point performs simple harmonic oscillation of period $T$ and the equation of motion is given by $x=Asin$$\left( {\omega t + \frac{\pi }{6}} \right)$. After the elapse of what fraction of the time period the velocity of the point will be equal to half of its maximum velocity?
A particle of mass m is executing oscillations about the origin on the $X-$axis. Its potential energy is $U(x) = k{[x]^3}$, where $k$ is a positive constant. If the amplitude of oscillation is $a$, then its time period $T$ is
A particle executes simple harmonic motion with an amplitude of $4 \mathrm{~cm}$. At the mean position, velocity of the particle is $10 \mathrm{~cm} / \mathrm{s}$. The distance of the particle from the mean position when its speed becomes $5 \mathrm{~cm} / \mathrm{s}$ is $\sqrt{\alpha} \mathrm{cm}$, where $\alpha=$____________.
For a particle executing simple harmonic motion, the kinetic energy $K$ is given by $K = {K_o}{\cos ^2}\omega t$. The maximum value of potential energy is
The particle executing $SHM$ of amplitude $'a'$ has displacement $-\frac {a}{2}$ at $t = \frac {T}{4}$ and a positive velocity. Find the initial phase of particle
A particle at the end of a spring executes simple harmonic motion with a period ${t_1}$, while the corresponding period for another spring is ${t_2}$. If the period of oscillation with the two springs in series is $T$, then
Two bodies of masses $1\, kg$ and $4\, kg$ are connected to a vertical spring, as shown in the figure. The smaller mass executes simple harmonic motion of angular frequency $25\, rad/s$, and amplitude $1.6\, cm$ while the bigger mass remains stationary on the ground. The maximum force exerted by the system on the floor is ..... $N$ ( take $g = 10\, ms^{-2}$)
A rectangular block of mass $5\,kg$ attached to a horizontal spiral spring executes simple harmonic motion of amplitude $1\,m$ and time period $3.14\,s$. The maximum force exerted by spring on block is $.......N$.
Abody performs simple harmonic oscillations along the straight line $ABCDE$ with $C$ as the midpoint of $AE.$ Its kinetic energies at $B$ and $D$ are each one fourth of its maximum value. If $AE = 2R,$ the distance between $B$ and $D$ is