Oscillations Te...

A particle vibrating simple harmonically has an acceleration of $$16{cms}^{-2}$$ when it is at a distance of $$4cm$$ from the mean position. Its time period is

The simple harmonic motion of a particle is given by $$x=a\sin 2\pi t$$. Then, the location of the particle from its mean position at a time $$1/8$$th of a second is:

A particle which is constrained to move along the x-axis, is subjected to a force in the same direction which varies with the distance $$x$$ of the particle from the origin is $$F(x)=-kx+a{ x }^{ 3 }$$. Here, $$k$$ and $$a$$ are positive constants. For $$x\ge 0$$, the functional form of the potential energy $${U}_{(x)}$$ of the particle is :

Which one of the following is simple harmonic?

A 2 kg block is dropped from a height $$ 0.4 m $$ on a spring of force constant $$k=1960 N/m$$.The maximum compression of spring is 

Four springs having the same force constant and a mass $$M$$ are connected between rigid walls as shown in figure. The system with smallest time period is

Velocity at mean position of a particle executing SHM is v, then velocity of the particle at a distance equal to half of the amplitude is

A spring with force constant $$k$$ is initially stretched by $$x_{1}$$. If it further stretched by $$x_{2}$$, then the increase in its potential energy is

The displacement of a particle in SHM is $$x=10\sin \begin{pmatrix}2t-\dfrac{\pi}{6}\end{pmatrix}m.$$ When its displacement is 6 m, the velocity of the particle (in $$ms^{-1}$$) is

Which one of the following represents simple harmonic motion ?