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Class XI Physics Oscillations 3

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Question 1

A particle of mass m is located in a potential field given by U(x) = U₀ (1 – cos ax) where U₀ and a are constants. The period of small oscillations is -

Question 2

A uniform rod of length η is suspended by an end and is made to undergo small oscillations. What is the length of a simple pendulum which has the same time period as that of the rod?

Question 3

Two pendulums have time-periods T and 5T/4. They start S.H.M. at the same time from the mean position. What will be the phase difference between them after the bigger pendulum has completed one oscillation?

Question 4

A diatomic molecule having masses m₁ and m₂ has its P.E. function about the equilibrium position r₀ as given by U(r) = –A + B(r – r₀)² where A and B are constants. When the atoms vibrate at high temperature conditions, the square of the angular frequency will be –

Question 5

A long uniform rod of length L, mass M is free to rotate in a horizontal plane about a vertical axis through its end. Two springs of constant K each are connected as shown. On equilibrium, the rod was horizontal. The frequency will be –

Question 6

Two bodies M and N of equal masses are suspended from two separate massless springs of spring constants k₁ and k₂ respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of M to that of N is-

Question 7

A weightless spring which has a force constant 'k' oscillates with frequency 'n' when a mass m is suspended from it. The spring is cut into two equal halves and a mass 2m is suspended from it. The frequency of oscillation will now become-

Question 8

If the distance between the centre of gravity and point of suspension of a compound pendulum is η and the radius of gyration about the axis passing through its centre of gravity is k, its time period will be infinite if-

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