Tag: free, damped and forced oscillations
Questions Related to free, damped and forced oscillations
The length and diameter of a metal wire is doubled. The fundamental frequency of vibration will change from '$n$' to (Tension being kept constant and material of both the wires is same)
In forced oscillation of a particle the amplitude is maximum for a frequency $\omega _1$ of force, while the energy is maximum for a frequency $\omega _2$ of the force, then:
A weightless spring has a force constant $k$ oscillates with frequency $f$ when a mass $m$ is suspended from it. The spring is cut into three equal parts and a mass $3\ m$ is suspended from it. The frequency of oscillation of one part will now becomes
If density (D) acceleration (a) and force (F) are taken as basic quantities,then Time period has dimensions
The potential energy of a particle of mass $1\ kg$ in motion along the $x-$axis is given by: $U=4(1-\cos 2x)\ l$, where $x$ is in metres. The period of small oscillations (in sec) is:
A sphere of radius r is kept on a concave mirror of radius of curvature R. The arrangement is kept on a horizontal table (the surface of concave mirror is frictionless and sliding not rolling). If the sphere is displaced from its equilibrium position and left, then it executes S.H.M. The period of oscillation will be
The amplitude of a damped oscillator decreases to 0.9 times its original magnitude is 5 s .In another 10 s it will decrease to $\alpha $ times its original magnitude where $\alpha $ equals :
Three infinitely long thin wires, each carrying current I in the same direction, are in the $x-y$ plane of a gravity free space. The central wire is along the y-axis while the other two are along $x=\pm\ d$.
(a) Find the locus of the points for which the magnetic field $B$ is zero.
(b) If the central wire is displaced along the z-direction by a small amount and released, show that it will execute simple harmonic motion. If the linear density of the wires is $\lambda$, find the frequency of oscillation.
A student performs an experiment for determination of $\Bigg \lgroup g = \frac{4\pi^2 l}{T^2} \Bigg \rgroup$, l = 1m, and he commits an error of $\Delta l$ For T he takes the time of n oscillations with the stop watch of least count $\Delta T$ and he commits a human error of 0.1 s. For which of the following data, the measurement of g will be most accurate?
A particle moves such that its acceleration is given by : $\alpha=-\beta(x-2)$
Here :$\beta$ is a positive constant and x the position from oigin. Time period of oscillations is: