Oscillations Te...

The position vector of a particle from origin is given by $$\hat r = A\left( {\hat i\cos \omega t + \hat jsin\omega t} \right)$$. The motion of the particle is

A particle is subjected to two simple harmonic motions given by:
$$y_1=10 \sin\omega t$$ and $$y_2=5 \sin (\omega t+ \pi)$$ The maximum speed of the particle is:

The maximum time period of oscillation of a simple pendulum of larger length is :

A particle is executing $$SHM$$ along $$x$$-axis given by $$x = A  \sin \omega t$$. The average velocity during the time interval $$t = 0$$ to $$t = T$$ is 

Two particles executes S.H.M along the same line at the same frequency. They move in opposite direction at the mean position. The phase difference will be :

A uniform straight rod of mass 'm; kg and length L is hinged at one end. It is free to oscillate in vertical plane. A point of mass (m kg) is attached to it at a distance 'x' from the hinge. The value of x for which time period of oscillations will be minimum is (use: $$\sqrt { \frac { 7 }{ 3 } =1.5 } $$)

A dog of mass $$m$$ is walking on a pivoted disc of radius $$R$$ and mass $$M$$ in a circle of radius $$R/2$$ with an angular frequency $$n$$. The disc will revolve in opposite direction with frequency :

A string of mass m is fixed at both ends. The fundamental tone oscillations are excited in the strong with angular frequency $$\omega $$ and maximum displacement amplitude A. Find the total energy curtained in the string.

In the arrangement as shown, the length of rod is L and mass is M and it is connected to smooth pin at O.The rod is placed on smooth horizontal table.The spring constant of both the spring is K.The rod is displaced by a small angle $$\theta$$ to perform small ocillation, then is given by