NIOS Class 12 Physics Chapter 13 Simple Harmonic Motion Solutions English Medium As Per New Syllabus to each chapter is provided in the list so that you can easily browse throughout different chapters NIOS Class 12 Physics Chapter 13 Simple Harmonic Motion Notes in English and select need one. NIOS Class 12 Physics Solutions English Medium Download PDF. NIOS Study Material of Class 12 Physics Notes Paper Code: 312.
NIOS Class 12 Physics Chapter 13 Simple Harmonic Motion
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Simple Harmonic Motion
Chapter: 13
| Module – IV: Oscillations and Waves |
INTEXT QUESTIONS 13.1
1. What is the difference between a periodic motion and an oscillatory motion?
Ans: The difference between periodic motion and oscillatory motion lies in the nature and type of movement involved:
Periodic motion is any motion that repeats itself at regular intervals of time. It does not necessarily involve back-and-forth movement. Examples of periodic motion include the revolution of the Earth around the Sun, the rotation of a fan, or the ticking of a clock. In these cases, the motion occurs in a cycle and repeats after a fixed period.
Oscillatory motion, however, is a specific type of periodic motion in which an object moves to and fro about a fixed point or position (called the mean or equilibrium position). Examples include the swinging of a pendulum, the motion of a spring, or vibrations of a tuning fork. In oscillatory motion, the object moves back and forth in a regular pattern, usually on either side of its mean position.
2. Which of the following examples represent a periodic motion?
(i) A bullet fired from a gun.
(ii) An electron revolving round the nucleus in an atom.
(iii) A vehicle moving with a uniform speed on a road.
(iv) A comet moving around the Sun.
(v) Motion of an oscillating mercury column in a U-tube.
Ans: Periodic motions:
(ii) An electron revolving round the nucleus in an atom
(iv) A comet moving around the Sun
(v) Motion of an oscillating mercury column in a U-tube
3. Give an example of (i) an oscillatory periodic motion and (ii) a non-oscillatory periodic motion.
Ans Here are the examples:
(i) Oscillatory periodic motion: The swinging of a pendulum is an example of oscillatory periodic motion. It moves back and forth about its mean position at regular intervals of time.
(ii) Non-oscillatory periodic motion: The motion of the Earth around the Sun is an example of non-oscillatory periodic motion. It repeats its path in a fixed time (one year) but does not move to and fro about a mean position, so it is not oscillatory.
INTEXT QUESTIONS 13.2
1. A small spherical ball of mass m is placed in contact with the surface on a smooth spherical bowl of radius r a little away from the bottom point. Calculate the time period of oscillations of the ball (Fig. 13.10).
Ans: Given: Restoring force, F = mg sin θ
≈ mg θ (for small θ)
For small θ,
θ = x/r
So, F = mg x / r
This force provides SHM since it is proportional to displacement and directed towards mean position.
Angular frequency,
omega = √{/{g}{r}}
2. A cylinder of mass m floats vertically in a liquid of density ρ. The length of the cylinder inside the liquid is l. Obtain an expression for the time period of its oscillations (Fig. 13.11).
Ans: Given: Upthrust = yαρg
Mass displaced,
m = αρ
So, equation of motion:
F = –αρg y
= –mω²y
So, ω2 = /{αρg}{m}
Given law of floatation, m = αρp
Therefore,
ω2 = g/l
Hence, T = 2π √{l/g}
3. Calculate the frequency of oscillation of the mass m connected to two rubber bands as shown in Fig. 13.12. The force constant of each band is k. (Fig. 13.12)
Ans: Given: Two identical rubber bands, each with force constant k
Both bands in parallel
Displacement = x
Combined force constant = 2k
Equation for SHM,
Restoring force = –(2k)x
Angular frequency,
Frequency,
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