Oscillations Te...

A particle of mass m is placed in a potential field U(x) =U₀ (1 – cos ax), where U₀ and a are positive constants. The time period of small oscillations would be

A wooden cube (density of wood d) of side l floats in a liquid of density p with its upper and lower surfaces horizontal. If the cube is pushed slightly down and released, its performs simple harmonics motion of period T, then T is equal

A particle of mass m is located in a one dimensional potential field where potential energy is given by, V(x) = A (1 – cos px),where A and p are constants. The period of small oscillations of the particle is

The periodic time of a particle doing simple harmonic motion is 4 s. The taken by it to go from its mean position to half the maximum displacement (amplitude) is

A particle executes linear simple harmonic motion with an amplitude of 2 cm. When the particle is at 1 cm from the mean position the magnitude of its velocity is equal to that of its acceleration. Then, its time period in sec is

A spring balance has a scale that reads from 0 to 60 kg. The length of the scale is 30 cm. A body suspended from this balance and when displaced are released, oscillates with a period of 0.8 s, what is the weight of the body when oscillating?

This question has Statement I and Statement H. Of the four choices given after the statements, choose the one that best describes the two statements.
If two springs S₁ and S₂ of force constants k₁ and k₂ , respectively are stretched by the same force, it is found that more work is done on the spring S₁ than on spring S₂ .
Statement I If stretched by the same amount, work done on S₁, will be more than that on S₂.
Statement II k₁ < k₂

If a simple pendulum has significant amplitude (upto a factor of 1/ e of original) only in the period between t = 0 s to t = τ s, then τ may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity with b as the constant of proportionality, the average life time of the pendulum is (assuming damping is small) in sec