Two identical pendulums oscillate with a constant phase difference $\frac{\pi}{4}$ and same amplitude. If the maximum velocity of one is $v$, the maximum velocity of the other will be ........
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- 1In a linear simple harmonic motion $(SHM)$View Solution
$(A)$ Restoring force is directly proportional to the displacement.
$(B)$ The acceleration and displacement are opposite in direction.
$(C)$ The velocity is maximum at mean position.
$(D)$ The acceleration is minimum at extreme points.
Choose the correct answer from the options given below :
- 2A particle of unit mass is moving along the $x$-axis under the influence of a force and its total energy is conserved. Four possible forms of the potential energy of the particle are given in column $I$ (a and $U _0$ are constants). Match the potential energies in column $I$ to the corresponding statement$(s)$ in column $II.$View Solution
column $I$ column $II$ $(A)$ $U _1( x )=\frac{ U _0}{2}\left[1-\left(\frac{ x }{ a }\right)^2\right]^2$ $(P)$ The force acting on the particle is zero at $x = a$. $(B)$ $U _2( x )=\frac{ U _0}{2}\left(\frac{ x }{ a }\right)^2$ $(Q)$ The force acting on the particle is zero at $x=0$. $(C)$ $U _3( x )=\frac{ U _0}{2}\left(\frac{ x }{ a }\right)^2 \exp \left[-\left(\frac{ x }{ a }\right)^2\right]$ $(R)$ The force acting on the particle is zero at $x =- a$. $(D)$ $U _4( x )=\frac{ U _0}{2}\left[\frac{ x }{ a }-\frac{1}{3}\left(\frac{ x }{ a }\right)^3\right]$ $(S)$ The particle experiences an attractive force towards $x =0$ in the region $| x |< a$. $(T)$ The particle with total energy $\frac{ U _0}{4}$ can oscillate about the point $x=-a$. - 3A ball is rolling without slipping in a spherical shallow bowl (radius $R$ ) as shown in the figure and is executing simple harmonic motion. If the radius of the ball is doubled, then the time period of oscillationView Solution
- 4The length of simple pendulum is increased by $44\%$. The percentage increase in its time period will be ..... $\%$View Solution
- 5The total energy of particle performing $S.H.M.$ depend onView Solution
- 6Out of the following functions representing motion of a particle which represents $SHM$View Solution
$(A)\;y= sin\omega t-cos\omega t$
$(B)\;y=sin^3\omega t$
$(C)\;y=5cos\left( {\frac{{3\pi }}{4} - 3\omega t} \right)$
$(D)\;y=1+\omega t+{\omega ^2}{t^2}$
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- 9A simple pendulum of length $ l$ has a brass bob attached at its lower end. Its period is $T$. If a steel bob of same size, having density $ x$ times that of brass, replaces the brass bob and its length is changed so that period becomes $2T$, then new length isView Solution
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