Oscillations Te...

A body executing SHM has its velocity $$10 cm/s$$ and $$7 cm/s$$ when its displacements from mean position are $$3 cm$$ and $$4 cm$$ respectively. The length of path is

The minimum phase difference between two SHM's is:
$$ y_{1}=\sin \left(\dfrac{\pi}{6}\right) \sin(\omega t)+\sin\left(\dfrac{\pi }{3}\right) \cos(\omega t )$$

$$ y_{2}=\cos\left(\dfrac{\pi}{6}\right) \sin(\omega t)+\sin \left(\dfrac{\pi}{3}\right) \cos(\omega t)$$ is:

A particle executes SHM in a straight line. The maximum speed of the particle during its motion is $$V_{max}$$. Then the average speed of the particle during the SHM is :

A 1 kg mass executes SHM with an amplitude 10 cm, it takes $$2\pi$$ seconds to go from one end to the other end. The magnitude of the force acting on it at any end is :

A body executes S.H.M. under the action of a force $$F$$$$_{1}$$ with a time period $$4/5$$ seconds. If the force is changed to $$F$$$$_{2}$$, it executes S.H.M. with a time period $$3/5$$ seconds. If both the forces $$F$$$$_{1}$$and $$F$$$$_{2}$$ act simultaneously in the same direction on the body, then its time period in seconds is:

A particle free to move along the x-axis has potential energy given by $$U(x)=k[1-exp\left ( -x^{2} \right )]$$ for$$-\infty \leq x\leq +\infty ,$$ where k is a positive constant of appropriate dimensions. Then:

A particle of mass $$m$$ is executing oscillations about the origin on the $$x$$-axis. It's potential energy is $$U(x)=k\left | x \right |^{3}$$, where $$k$$ is a positive constant. If the amplitude of oscillation is $$a$$, then its time period $$T$$ is:

A body of mass 1/4 kg is in S.H.M and its displacement is given by the relation $$y= 0.05 sin(20t+\dfrac{\pi }{2})$$ m. If $$t$$ is in seconds, the maximum force acting on the particle is:

Two particles are in S.H.M. along parallel straight lines with same amplitude and time period. If they cross each other in opposite directions at the midpoint of mean and extreme positions. Phase difference between them is:

A disc of mass $$M$$ is attached to a horizontal massless spring of force constant $$K$$ so that it can roll without slipping along a horizontal surface. If the disc is pushed a little towards right and then released, its center of mass executes SHM with a period of