“Acceleration, Velocity and Displacement of SHM” MHT-CET Class 12 Physics Crash Course | Chapter Oscillations
In this session G.S. Khairnar discussed the theory and MCQ’s of “Acceleration, Velocity and Displacement of SHM”. The session will be useful for all the aspirants of MHT-CET 2022. The session will be in Marathi and English.
Acceleration, Velocity and Displacement of SHM:-
Dear students in previous article we have learnt about the concept of linear simple harmonic motion and the differential equation of linear SHM. The differential equation for a particle of mass ‘m’ performing oscillatory motion is given as,
Where, x is displacement of particle and ω is angular frequency of SHM.
Using the above equation we are going to derive expressions for the acceleration, velocity and displacement of particle performing linear SHM.
Let’s derive the formulae for acceleration and velocity in linear SHM…….!
(1) Acceleration in SHM:-
We know the differential equation of SHM is,
From above equation we can conclude that acceleration in SHM is directly proportional to the displacement, and acts in opposite direction of displacement.
(2) Velocity in SHM:-
Using equation for acceleration, we can find out the velocity of particle in SHM as follows,
Then equation (2) becomes,
When particle is at extreme position, x=a and v=0, then value of C can be written as,
This is an equation for velocity of particle performing linear SHM, where is angular frequency.
(3) Displacement of particle in SHM
The velocity is rate of change of displacement.
Where is constant off integration.
This is the equation of displacement of particle performing linear simple harmonic motion.
Maximum and minimum values for acceleration and velocity:-
Acceleration, Velocity and Displacement of SHM:-
Let’s solve some MCQ’s……!
Q.1) The maximum velocity of particle performing SHM of amplitude 8 cm and period of 2.4 π se c is….
a) 6.67 cm/s
b) 6.67 m/s
c) 66.7 cm/s
d) 66.7 m/s
Answer
a) 6.67 cm/s
Q.2) The displacement of particle performing linear SHM at extreme position is given as….
a) x=a sin ωt
b) x=a cos ωt
c) x=a tan ωt
d) x=a sec ωt
Answer
b) x=a cos ωt
Q.3) Maximum values of acceleration and velocity of particle performing the linear SHM is 12 cm/s2 and 3 cm/s respectively. The period of SHM is……
a) 0.157 s
b) 1.57 s
c) 15.7 s
d) 157 s
Answer
b) 1.57 s
Q.4) A particle performing SHM of period 6 s starts from extreme position. Time required reaching the particle at 4 cm from mean position if the amplitude of SHM is 8 cm.……
a) 1 s
b) 10 s
c) 2 s
d) 20 s
Answer
a) 1 s
Q.5) The velocity of particle in SHM at distance of 7 cm from the mean position when amplitude is 12 cm and period of 3π s is ……
a) 65 m/s
b) 65 cm/s
c) 6.5 m/s
d) 6.5 cm/s
Answer
d) 6.5 cm/s
Q.6) Which among the following statement is true in case of linear SHM?
a) Acceleation of particle in SHM is minimum at extreme position
b) Velocity of particle in SHM is maximum at extreme position
c) Acceleation of particle in SHM is maximum at mean position
d) Velocity of particle in SHM is minimum at extreme position
Answer
b) Velocity of particle in SHM is maximum at extreme position
