The angular frequency of the damped oscillator is given by $\omega =\sqrt { \left( \dfrac { k }{ m } -\dfrac { { r }^{ 2 } }{ 4{ m }^{ 2 } } \right) }$ , where k is the spring constant, $m$ is the mass of the oscillator and $r$ is the damping constant. If the ratio $\dfrac { { r }^{ 2 } }{ mk }$ is $80$%, the change in time period compared to the undamped oscillator is approximately as follows:
In case of a forced vibration, the resonance wave becomes very sharp when the :
The potential energy of a particle of mass 1 kg in motion along the x-axis is given by U = 4(1 - cos2x) J. Here x is in meter. The period of small oscillations (in sec) is _______.
The period of oscillation of a simple pendulum of constant length is independent of
Assertion : In damped oscillations, the energy of the system is dissipated continuously.
Reason : For the small damping, the oscillations remain approximately periodic.
Assertion : In forced oscillations, the steady state motion of the particle is simple harmonic.
Reason : Then the frequency of particle after the free oscillations die out, is the natural frequency of the particle.
A force F= -4x-8 is acting on a block where x is position of block in meter. The energy of oscillation is 32 J, the block oscillate between two points Position of extreme position is:
A block of $0.5\ kg$ is placed on a horizontal platform. The system is making vertical oscillations about a fixed point with a frequency of $0.5\ Hz.$ Find the maximum amplitude of oscillation if the block is not to lose contact with the horizontal platform?
A highly rigid cubical block A of small mass M and side L is fixed rigidly on another cubical block B of the same dimensions and of low modulus of rigidity $\eta $ such that the lower face of A completely covers the upper face of B. The lower face of B is rigidly held on horizontal surface. A small force is applied perpendicular to the side faces of A. After the force is withdrawn, block A executes small oscillations the time period of which is given by