“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 “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.
Linear Simple Harmonic Motion:-
Hello students in this lesson we are going to study about important type of motion viz; oscillatory motion. Lets define some important concepts.
- Periodic Motion:-
A motion which repeats itself in equal intervals of time is called periodic motion.
The time taken by the particle to complete one oscillation is called periodic time.
- Oscillatory Motion:-
The motion of body is along the same path i.e. towards left of mean position and then towards right (to and fro). Such type of motion is called as oscillatory motion. One complete set of such motion is called as an ‘Oscillation’. The basic form of oscillatory motion is nothing but simple harmonic motion.
E.g-i) The motion of pendulum in a clock.
- ii) Motion of balance wheel of a watch.
Let’s learn the concept in detail…..!
Consider a spring of mass ‘m’ kept on horizontal surface whose one end is fixed to wall and hanger is attached to its end through frictionless pulley as shown in a fig.
When load in the hanger increases, it is observed that the spring gets stretched up to point A and then moves back to mean position and then to another point B. This indicates that the spring is oscillating about mean position with points A and B as extreme position under action of restoring force of spring and repeats periodically. Such type of motion is known as simple harmonic motion.
Let ‘x’ be the displacement of particles of spring from the mean position which is function of time and given as,
∴ x =a sin(ωt+ α)
Where ‘a’ is amplitude of motion,
‘ω’ is angular frequency and α is phase of oscillation
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,
Linear Simple Harmonic Motion:-
Let’s solve some MCQ’s….!
Q.1) The motion which repeats itself after fixed interval of time is called as….
a) linear motion
b) non uniform motion
c) periodic motion
d) random motion
Answer
c) periodic motion
Q.2) Which among the following is an example of oscillatory motion?
a) motion of pendulum in a clock.
b) motion of planets around sun
c) motion of electrons around the nucleus
d) all of above
Answer
a) motion of pendulum in a clock.
Q.3) The linear simple harmonic motion is the periodic motion in which….
a) restoring force always acts towards the mean position
b) magnitude of restoring force is directly proportional to displacement
c) restoring force and displacement are opposite to each other.
d) all of above
Answer
d) all of above
Q.4) SI unit of force constant is….
a) m
b) N/m
c) m/N
d) None of above
Answer
b) N/m
Q.5) A particle of mass 20 g performing the linear SHM with angular frequency of 24 and displaced through 36 cm from mean position. Restoring force acting on the particle is….
a) 1 N
b) 1 dyne
c) 41 N
d) 41 dyne
Answer
d) 41 dyne
Here, m= 20 g= 0.02 kg, ω= 24π rad/s, and x= 36 cm=0.36 cm.
We have, F= kx = mω2x =0.02 ×24π× 24π×0.36=40.88=41 N
