Oscillations Te...

If a particle is acted by two simple harmonic motions simultaneously, the path of particle is:

For a simple pendulum, the graph between $$T^2$$ and $$L$$ is:

The equations of two linear S.H.M.'s are
$$x=a\sin \omega t$$ along x-axis
$$y=a\sin 2\omega t$$ along y-axis
If they act on a particle simultaneously, the trajectory of the particle is:

A body with speed '$$v$$' is moving along a straight line. At the same time it is at distance $$x$$ from a fixed point on the line, the speed is given by $$v^2=144-9x^2$$. Then:

A point mass $$m=20kg$$, is suspended by a massless spring of constant $$2000 N/m$$. The point mass is released when elongation in the spring is $$15cm$$. The equation of displacement of particle as function of time is: (Take $$g=10 m/s^2$$)

A naughty boy is sitting on the roof of a flat toy car of mass $$6$$ kg. If no slipping takes place between car and the boy then what should be the mass of the child in order to have period of system equal to $$0.758$$ sec?

A spring of spring constant $$200N/m$$ has a block of mass $$1 kg$$ hanging at its one end and of other end spring is attached to a ceiling of an elevator. The elevator rising upwards with an acceleration of $$g/3$$. When acceleration is suddenly cease, then what should be the angular frequency and elongation during the time when the elevator is accelerating?

There are two pendulums of length $$l_1$$ and $$l_2$$ which start vibrating. At some instant, the both pendulum are in mean position in the same phase. After how many vibrations of shorter pendulum, the both pendulum will be in phase in the mean position?
$$[(l_1 > l_2), l_1=121 cm, l_2=100 cm]$$

A particle of mass m is allowed to oscillate near the minimum of a vertical parabolic path having the equation $$x^2=4ay$$. The angular frequency of small oscillations is given by:

Figure represents two simple harmonic motions.
The parameter which has different value in the two motions is