Oscillations Te...

A particle of mass m is attached to a spring ( of spring constant k) and has a natural angular frequency ω₀. An external force F (t) proportional to cos ωt(ω ≠ ω₀) is applied to the oscillator. The time displacement of the oscillator will be proportional to

An ideal spring with spring-constant K is hung from the ceiling and a block of mass M is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is

The displacement y of a particle executing periodic motion is given by y = 4 cos² (t/2) sin (1000 t). This expression may be considered to be a result of the superposition of .... independent harmonic motions

The function sin² (ωt) represents

A brass cube of side a and density σ is floating in mercury of density ρ. If the cube is displaced a bit vertically, it executes S.H.M. Its time period will be

Two identical balls A and B each of mass 0.1 kg are attached to two identical massless springs. The spring mass system is constrained to move inside a rigid smooth pipe bent in the form of a circle as shown in the figure. The pipe is fixed in a horizontal plane. The centres of the balls can move in a circle of radius 0.06 m. Each spring has a natural length of 0.06 π m and force constant 0.1 N/m. Initially both the balls are displaced by an angle θ = π/6 radian with respect to the diameter PQ of the circle and released from rest. the frequency of oscillation of the ball B is

A disc of radius R and mass M is pivoted at the rim and is set for small oscillations. If simple pendulum has to have the same period as that of the disc, the length of the simple pendulum should be

One end of a spring of force constant k is fixed to a vertical wall and the other to a block of mass m resting on a smooth horizontal surface. There is another wall at a distance x₀ from the block. The spring is then compressed by 2 x₀ and released. The time taken to strike the wall is