A function is represented by equation$y = A\,\cos \,\omega t\,\cos \,2\omega t + A\,\sin \,\omega t\,\sin \,2\omega t$.
Than the nature of the function is
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A simple pendulum of mass $m$ executes $S.H.M.$ with total energy $E$. If at an instant it is at one of extreme positions, then its linear momentum after a phase shift of $\frac{\pi}{3} \,rad$ will be
An oscillator of mass $M$ is at rest in its equilibrium position in a potential $V\, = \,\frac{1}{2}\,k{(x - X)^2}.$ A particle of mass $m$ comes from right with speed $u$ and collides completely inelastically with $M$ and sticks to it . This process repeats every time the oscillator crosses its equilibrium position .The amplitude of oscillations after $13$ collisions is: $(M = 10,\, m = 5,\, u = 1,\, k = 1 ).$
Two masses, both equal to $100\, g$, are suspended at the ends of identical light strings of length $\lambda = 1.0\, m$, attached to the same point on the ceiling (see figure). At time $t = 0$, they are simultaneously released from rest, one at angle $\theta_1 = 1^o$, the other at angle $\theta_2 = 2^o$ from the vertical. The masses will collide
A particle executes a simple harmonic motion of time period $T$. Find the time taken by the particle to go directly from its mean position to half the amplitude
A mass $m$ is attached to two springs as shown in figure. The spring constants of two springs are $K _1$ and $K _2$. For the frictionless surface, the time period of oscillation of mass $m$ is
A body executes sample harmonic motion under the action of a force $F_1$ with a time period $(4 / 5)\ sec$. If the force is changed to $F_ 2$ it executes $SHM$ with time period $(3 / 5)\ sec$. If both the forces $F_1$ and $F_2$ act simultaneously in the same direction on the body, it's time period (in $second$) is
A simple pendulum with length $100\,cm$ and bob of mass $250\,g$ is executing S.H.M. of amplitude $10\,cm$. The maximum tension in the string is found to be $\frac{x}{40}\,N$. The value of $x$ is $..........$.
If the particle repeats its motion after a fixed time interval of $8 \,s$ then after how much time its maximum value of $PE$ will be attained after attaining its minimum value is ........... $s$