EASY
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What is phase and initial phase?

Important Questions on Oscillations

MEDIUM
The function (sinωt-cosωt) represents the S.H.M having a time period T
HARD

A load of mass m falls from a height h on the scale pan hung from a spring as shown. If the spring constant is k and the mass of the scale pan is zero and the mass m does not bounce relative to the pan, then the amplitude of vibration is 

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MEDIUM
A simple harmonic oscillator of frequency 1 Hz has a phase of 1 radian. By how much should the origin be shifted in time so as to make the phase of the oscillator vanish. (time in seconds).
EASY
Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance R2 from the earth's centre, where R is the radius of the earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel, it will execute a simple harmonic motion with a time period:
EASY
A particle is performing SHM starting from extreme position. Graphical representation shows that, between displacement and acceleration, there is a phase difference of
MEDIUM
An object was found to make oscillations governed by the equation y=cos2ωt+π4-0.5. The amplitude and angular frequency of these oscillations, respectively, are
MEDIUM
Frequency of oscillation of a body is 5 Hz when a force F1 is applied and 12 Hz when another force F2 is applied. If both forces F1 and F2 are applied together, then frequency of oscillation of the body will be
MEDIUM
A wave along a string has the following equation y=0.05sin(28t-1.78x) m (where, t is in seconds and x is in meters). What are the amplitude (A), frequency (f) and wavelength (λ) of the wave ?
HARD

An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M. The piston and the cylinder have equal cross-sectional area A. When the piston is in equilibrium, the volume of the gas is V0 and its pressure is M0. The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency
[Assume the system is in space.]

HARD
A particle executes simple harmonic motion and it is located at x=a, b and c at time t0, 2t0 and 3t0 respectively. The frequency of the oscillation is:
EASY
A particle performs simple harmonic motion with a period of 2 second. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is 1a s. The value of a to the nearest integer is
EASY
A simple pendulum of length L has mass M and it oscillates freely with amplitude A. At the extreme position, its potential energy is (g = acceleration due to gravity)
EASY
The function of time representing a simple harmonic motion with a period of πω is :
EASY
A mass M is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes S.H.M. of period T. If the mass is increased by m, the time period becomes 5T3. What is the ratio Mm?
MEDIUM

A simple pendulum suspended from the ceiling of a stationary lift has a time period T0. When the lift descends at uniform speed, the time period is T1. When the lift descends with constant acceleration, the time period is T2. Which of the following is correct?

MEDIUM
A body of mass 1 kg is made to oscillate on a spring of force constant 15 N/m. Calculate the angular frequency 
MEDIUM
A body of mass 1 kg is made to oscillate on a spring of force constant 15 N/m. Calculate the frequency of vibrations. 
HARD

Match ListI (Event) with ListII (Order of the time interval for the happening of the event) and select the correct option from the options given below the lists.

  List-I   List-II
(a) The rotation period of earth (i) 105 s
(b) Revolution period of earth  (ii) 107 s
(c) Period of a light wave  (iii) 10-15 s
(d) Period of a sound wave  (iv) 10-3 s
EASY
The weight suspended from a spring oscillates up and down. The acceleration of weight will be zero at
EASY
A particle of mass m is moving along the x-axis under the potential  V(x)= k x 2 2 + λ x  where k and  x are positive constants of appropriate dimensions. The particle is slightly displaced from its equilibrium position. The particle oscillates with the angular frequency ω given by