“Composition of SHM” MHT-CET Class 12 Physics Crash Course | Chapter Oscillations
In this session G.S. Khairnar discussed the theory and MCQ’s of “Composition of SHM”. The session will be useful for all the aspirants of MHT-CET 2022. The session will be in Marathi and English.
Composition of SHM:-
Hello dear students we are familiar about the principle of superposition. According to this principle the resultant displacement of waves can be obtained by the vector sum of their individual displacements. In this article we are going to prove that, if two simple harmonic waves are overlapped, the resultant wave obtained is also simple harmonic progressive wave.
Let’s illustrate the concept……..!
Definition:
Composition of two SHM’s of same period along with same straight line (Analytical treatment):-
Consider two SHM’s of same period and frequencies but slightly different amplitudes a1, a2 and initial phase’s α1, α2 travelling along same direction produces displacement given as,
x1=a1 sin (ωt+a1 ) .…..(1)
x2=a2 sin (ωt+a2)…….(2)
The resultant displacement by principal of superposition is given as,
Equation (5) shows that the resultant displacement of two motions is SHM whose amplitude is R and initial phaseδ.
- Amplitude (R) of resultant motion:-
Squaring and adding equations (3) and (4) we get,
This is the required expression for resultant amplitude of SHM.
- Phase (δ) of resultant motion:-
- Some important conditions:-
Composition of SHM:-
Let’s solve some MCQ’s…..!
Q.1) The resultant of two SHM’s of equal amplitude overlapped with the phase difference of π radian is….
a) a/2
b) a
c) 2a
d) 0
Answer
d) 0
Q.2) The resultant of two SHM’s of equal amplitude overlapped with the phase difference of 0 radian is….
a) a/2
b) a
c) 2a
d) 0
Answer
c) 2a
Q.3) Two simple harmonic waves of amplitude 4 cm and 6 cm overlapped at right angles, the resultant of these waves will be….
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