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Revision Quiz | Oscillations

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Question 1

A block attached to a spring moves on a horizontal table with the small coefficient of friction such that it executes damped oscillatory motion. The amplitude as a function of time decreases

Question 2

The instantaneous position x(t) of a small block performing one-dimensional damped oscillation is

. Here ω is angular frequency, ϒ is damping coefficient, A is the initial amplitude, and

is initial phase. If

and

, the values of A and

(with n =0,1,2,….) are

Question 3

A 2.5 cm thin rod of mass 100g is suspended from its midpoint from a long wire. Its period of angular SHM is measured to be 2s. An object is then hung from the same wire and its period is found to be 4s. What is the rotational inertia of object about its suspension axis?

Question 4

A spring-mass system has an un-damped natural angular frequency

. The solution x(t) at critical damping is given by

where x₀ constant. The system experiences the maximum damping force at the time.

Question 5

Two masses m and 2m are connected with a spring of spring constant k and length d is kept at rest on a friction less plane. What will be the shortest distance between the masses when at t=0 mass m is pushed with a velocity v towards the second mass.

Question 6

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 7

Four springs of constant as shown are attached to a pair of masses m each as shown. The time period will be 2π times-

Question 8

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 9

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 10

A simple pendulum and a Seconds pendulum starts swinging in phase. They swing in phase again after an interval of 18 second. What is the time period (in sec) of the simple pendulum?

Question 11

Three S.H.M. of equal amplitude A and equal time period in the same direction combine. The difference in phase between each pair is 60 ° ahead of the other. The amplitude of the resultant oscillation is –

Question 12

Two S.H.M’s of unequal amplitude with same frequency (act) on a particle at right angles, with a phase difference of π/2. The resultant motion is –

Question 13

A mass M is suspended from a spring of negligible mass. The spring is pulled is a little and then released so that the mass executes simple harmonic oscillations with a time-period T. If the mass is increased by m, then the time period becomes

. The ratio of (m/M) is -

Question 14

The displacement of a particle in S. H. M. varies according to the relation x= 4 (cos $Description: E:\WBJEE\2011\2011_Physics_files\image142.png$ t+sin $Description: E:\WBJEE\2011\2011_Physics_files\image142.png$ t). The amplitude of the particle is

Question 15

What will be the maximum acceleration of an object of mass 30 mg attached to a spring performing SHM if SHM is given by

, where 8 is in cms?

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Sep 26JEE & BITSAT