“Energy of Particle in SHM” MHT-CET Class 12 Physics Crash Course | Chapter Oscillations
In this session G.S. Khairnar discussed the theory and MCQ’s of “Energy of Particle in SHM”. The session will be useful for all the aspirants of MHT-CET 2022. The session will be in Marathi and English.
Energy of Particle in Simple Harmonic Motion:-
Hey students we know that, the particle performing linear SHM vibrates about its mean position, so that it possess mass and velocity. Due to this the particle performing linear SHM is said to have the potential energy as well as kinetic energy. The total energy of particle then can be obtained by taking sum of its kinetic energy and potential energy.
Let’s obtain the energy for particle in linear SHM……..!
Kinetic energy of particle in linear SHM:-
Consider a particle of mass m performing linear SHM with angular velocity ω. Let x be the displacement of particle from its mean position, as shown in fig below.
Let the particle at any point P at distance ‘x’ from O, then KE of particle is,
On substituting in above equation we get,
Equation (A) gives the kinetic energy of particle performing linear SHM.
Potential energy of particle in linear SHM:-
When particle is at point P, it is acted upon by restoring force directed towards mean position. The particle is displaced through small distance ‘dx’ against the restoring force. The small work done is,
∴ dW=-Fdx…….(3)
The negative sign indicates that work done is against the restoring force.
In SHM, F=-kx
∴ dW=k x dx ……(4)
The total work done can be obtain by integrating the equation (2) from 0 to x.
Total energy of particle in linear SHM:-
The total energy of particle performing SHM is sum of its KE and PE.
∴ Total energy=Kinetic energy + Potential energy
On substituting the values of KE and PE we get from equation (2) and (5) we get,
The above equation gives the total energy of particle performing linear SHM.
Some important points……….!
(1) total energy is directly proportional to
- Square of amplitude (a2)
- Square of frequency of particle (n2)
(2) Total energy of particle in SHM is nothing but kinetic energy at mean position,
i.e.
(3) Total energy of particle in SHM is nothing but potential energy at extreme position,
Energy of Particle in Simple Harmonic Motion:-
Let’s solve the MCQ’s on Energy of particle in SHM…!
Q.1) The total energy of particle performing the linear SHM is…..
a) Square of amplitude
b) frequency of particle
c) mass of particle
d) all of these
Answer
a) Square of amplitude
Q.2) If the particle is at extreme position of SHM having amplitude ‘A’, then the total energy of particle is nothing but…..
a) kinetic energy only
b) partly kinetic and partly potential
c) potential energy only
d) all of these
Answer
c) potential energy only
Q.3) Total energy of particle performing SHM at any point is…..
a) maximum at extreme position
b) maximum at mean position
c) constant at all the positions
d) cannot predicted
Answer
c) constant at all the positions
Q.4) Particle of mass 50 g performs linear SHM of amplitude 12 cm. If the frequency if oscillations of particle is 25 Hz, the total energy of particle is…..
a) 8.9 J
b) 89 J
c) 8.9 erg
d) 89 erg
Answer
a) 8.9 J
Q.5) The ratio of amplitudes and frequency of particles of same masses is 2:3 and 4:5. The ratio of total energies of particles is…..
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