Equation of SHM

IMPORTANT

Equation of SHM: Overview

This Topic covers sub-topics such as Simple Harmonic Motion, Amplitude, Phase, Periodic Motion, Oscillatory Motion, Angular Frequency, Definition of SHM, Mean Position, Equation of SHM, Restoring Force, Angular SHM and, Linear SHM

Important Questions on Equation of SHM

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Electrons moving with different speeds enter a uniform magnetic field in a direction perpendicular field. They will move along circular paths, time periods of rotation will be :

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The x-t graph of a particle undergoing simple harmonic motion is as shown in the figure.
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The acceleration of the particle at t=43 s is

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Two particles are performing SHM in same phase. It means that:
 

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A particle of mass 'm' is under an influence of a force F=-kx+F0. The particle when disturbed will oscillate ___

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Ratio of maximum acceleration to the maximum velocity of a simple harmonic oscillator is

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A particle executing simple harmonic motion has a maximum speed of 40 m·s-1 and maximum acceleration of 60 m·s-2. The period of oscillation is

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The displacement of a simple harmonic motion of amplitude 6 cm when its kinetic energy is equal to its potential energy is

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Match the following entries in column-I and column-II with respect to an oscillating spring-block system:

  column-I   column-II
(a) Mass of the block is doubled (i) Energy of oscillation becomes 4 times
(b) Spring constant is made 4 times (ii) Speed of block becomes 2 times
(c) Amplitude of oscillations is doubled (iii) P.E. becomes 4 times
(d) Angular frequency is doubled (iv) Time period becomes 2 times

 

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A simple harmonic oscillation is represented by x=Acosωt+π4. Its speed is maximum when 't' equals

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A particle of mass 0.4 kg executes simple harmonic motion of amplitude 0.4 m. When it passes through the mean position, its kinetic energy is 256×10-3 J. If the initial phase of the oscillation is π4, then the equation of its motion is ______

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Thus, simple harmonic motion (SHM) is not any periodic motion but one in which displacement is sinusoidal function of time.

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Two SHM’s are respectively by y=a1sin(ωtkx) and y=a2cos(ωtkx). The phase difference between the two is

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When a spring-mass system vibrates with simple harmonic motion, the mass in motion reaches its maximum velocity when its acceleration is _____ (maximum\minimum).

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A block of mass m=4 kg undergoes simple harmonic motion with amplitude A= 6 cm on the frictionless surface. Block is attached to a spring of force constant k=400 N m-1 . If the block is at x=6 cm at time t=0 and equilibrium position is at x=0 then the blocks position as a function of time (with x in centimetres and t in seconds) ?

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A mass of 36 kg is kept vertically on the top of a massless spring. What is the maximum compression of the spring if the spring constant is 15000 N/m. Assume g = 10m/s2.

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Suppose a particle P is moving uniformly on a circle of radius A with the angular speed ω . The sense of rotation is anticlockwise. If the  t=0 , it  makes an angle of ϕ with the positive direction of the x-axis. In time t, it will cover a further angle ωt.What is the projection of position vector on the X-axis at time t.

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If we tie a stone to the end of a string and move it with a constant angular speed in a horizontal plane about fixed point, the stone would perform a : 

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If the particle is moving in circular motion under SHM, then its x-projection is depending upon

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The x-projection for a certain particle in circular motion under SHM with period of 2 s, amplitude of oscillation is 2 m and initial phase of π2 is

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Which of the following conditions is not sufficient for S.H.M. and why?