“Differential Equation Of Linear Simple Harmonic Motion” MHT-CET Class 12 Physics Crash Course | Chapter Oscillations
In this session G.S. Khairnar discussed the theory and MCQ’s of “Differential Equation Of Linear Simple Harmonic Motion”. The session will be useful for all the aspirants of MHT-CET 2022. The session will be in Marathi and English.
Differential Equation Of Linear Simple Harmonic Motion:-
Dear students in previous article we have learnt about the concept of linear simple harmonic motion. Then the linear simple harmonic motion is defined as, the linear periodic motion of a body, in which the restoring force or acceleration is always directed towards the mean position and is of magnitude proportional to the displacement from the mean position, is called linear SHM.
i.e. F α –x
F= -kx
Where K is constant called force constant. In magnitude,
k= F/x
Let’s obtain the differential equation for linear simple harmonic motion…..!
Consider a particle of mass m performing linear SHM with angular velocity ω. Let x be the displacement of particle from its mean position.
Then the restoring force acting on the particle is given as,
F= -Kx……..(1)
Also by Newton’s 2nd law of motion,
F = ma ……..(2)
From equations (1) and (2) we get,
ma = -kx……..(3)
Now the acceleration of the particle is given as,
Differential Equation Of Linear Simple Harmonic Motion:-
Let’s solve some MCQ’s….!
Q.1) The differential equation of linear SHM particle of mass ‘m’ and displaced by ‘x’ is given as,
a) acceleration of SHM
b) angular frequency of SHM
c) angular velocity of SHM
d) linear velocity of SHM
Answer
a) acceleration of SHM
Q.5) Particle of 200 g performing linear SHM with period of π sec. The differential equation can be represented as…….
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