Oscillations Te...

The maximum velocity of a particle, executing simple harmonic motion with an amplitude $$7$$ mm, is $$4.4$$ m/s. The period of oscillation is :

A particle is executing SHM with amplitude of 4 cm and has a maximum velocity of 10 cm/sec.
(a) At what displacement its velocity is 4 cm/sec?
(b) What is its velocity at displacement 2 cm?

If two springs of spring constant $$k_1$$ and $$k_2$$ are connected together in parallel, the effective spring constant will be

A small solid cylinder of mass M attached to a horizontal massless spring can roll without slipping along a horizontal surface. find its time period.

A body executing $$S.H.M.$$ along a straight line has a velocity of $$3\ ms^{-1}$$ when it is at a distance of $$4\ m$$ from its mean position and $$4\ ms^{-1}$$ when it is at  a distance of $$3\ m$$ from its mean position. Its angular frequency and amplitude are:

Two particles $$A$$ and $$B$$ of equal masses are suspended from two massless springs of spring constants $$k_1$$ and $$k_2$$ respectively. If the maximum velocities, during oscillations, are equal, the ratio of amplitudes of $$A$$ and $$B$$ is :

The acceleration displacement $$(a-x)$$ graph of a particle executing simple harmonic motion is shown in the figure. Find the frequency of oscillation.

A particle executes SHM with a time period of 12 s. Find the time taken by the particle to go directly from its mean position to half of its amplitude.

A simple harmonic motion along the $$x$$-axis has the following properties: amplitude = $$0.5\ m$$, the time to go from one extreme position to other is, $$2\ s$$ and $$x = 0.3\ m$$ at $$t = 0.5\ s$$. The general equation of the simple harmonic motion is

The elastic potential energy of a stretched spring is given by $$E=50{x}^{2}$$ where $$x$$ is the displacement in meter and $$E$$ is in joule, then the force constant of the spring is