In mechanics, simple harmonic motion (SHM) is a special case of periodic motion. Here, the restoring force on the travelling body is directly proportional to the magnitude of the body’s displacement and exerts towards the equilibrium position of the body. It generates an oscillation, which is in motion indefinitely if no external force or friction slows it down. SHM can serve as mathematical representations of several types of motions, but is exemplified by the oscillation of weight on a spring when it is under linear elastic restoring force provided by Hooke’s law. This motion is sinusoidal in time quantity and shows one resonant frequency. Other motions can be modelled by SHM, including the simple pendulum motion; the net force on the body at the pendulum’s end must be proportional to the resultant displacement (it is only a good approximation when the swing angle is small). SHM can also be applied to molecular vibration.
In every scenario, the time interval for the cycle or repetition of the motion is known as a period, while the frequency is the number of periods per unit time. Thus, the period of the revolution of the Earth is one year (365 Earth days), and one orbit per year is the frequency. Interestingly, simple harmonic motion is a distinct instance of periodic motion. From the above examples, the water wave, the swing and the tuning fork perform simple harmonic motions. On the other hand, the revolution of the Earth and the bouncing ball do not follow the principles of harmonic motion. Waves that can be represented by sine curves are always periodic. If waves are propagated with a wavelength λ and a velocity v, then the value of period T is equivalent to the given wavelength divided by velocity (T = λ/v). We also know that frequency f is exactly reciprocal to the period of the wave; therefore, f = 1/T = v/λ.
Simple Harmonic Motion Questions and Answers
1) What is meant by periodic motion?
A periodic motion is a kind of motion which is repeated in recurring time intervals. Some familiar periodic motions are the Earth orbiting around the Earth, vibrating tuning forks, water waves, oscillating pendulums, and swings in motion.
2) What is meant by simple harmonic motion?
Simple Harmonic Motion (SHM) is a type of periodic motion in which the activated restoring force is directly proportional to the body’s displacement from its default position. The trajectory of the restoring force is always the side of the mean location. The acceleration of a body performing simple harmonic motion is described by a(t) = -ω<sup>2</sup> x(t). The symbol ω is the oscillating body’s angular velocity. Every SHMs is oscillatory and periodic in nature but not every oscillatory motion is SHM. The oscillatory motion is also known as the harmonic motion of every oscillatory motion, whereas the most prominent one is SHM or simple harmonic motion.
3) What is meant by linear simple harmonic motion (linear SHM)?
When a body moves to and fro about a constant point (known as equilibrium position) across a straight line, then the body’s motion is known as linear simple harmonic motion or linear SHM.
4) What are the unique features of simple harmonic motion?
Simple harmonic motion is a unique scenario of oscillation along with a straight line between the two furthest points (the trajectory of SHM is a constraint).
The path of the body must be a straight line. There will always be (until the external forces overpower the system) restoring force acting towards the mean position or equilibrium position. In simple harmonic motion, the mean position is a stable equilibrium.
5) What are the main types of simple harmonic motion?
Simple harmonic motion (SHM) can be categorised into two types:
- Linear SHM
- Angular SHM
6) What is meant by angular simple harmonic motion?
When a body oscillates angular long with respect to a stable axis, then its motion is known as angular SHM or angular simple harmonic motion.
7) What is meant by the time period of SHM?
The minimum time range after which the body stays repeating its movement is called the time period. In other words, it is the shortest time required to finish one full oscillation.
8) What is meant by phase difference?
The variation of total phase angles of two bodies performing SHM with respect to the default or mean position is called the phase difference.
9) What is the geometrical description of simple harmonic motion?
If a body is travelling with uniform speed along a circle’s circumference, then the straight line motion of the base of the perpendicular constructed from the body on the circle’s diameter is known as simple harmonic motion.
10) What is the main connection between simple harmonic motion and harmonic motion?
The harmonic motion is when the restoring force is proportional to the ​displacement but in opposite directions. On the other hand, simple harmonic motion is a type of harmonic motion with a fixed amplitude and an identical frequency.
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Practice Questions
1) What is meant by motion?
2) What is the relationship between simple harmonic motion and periodic motion?
3) What is the main difference between horizontal and vertical motion?
4) What are the applications of periodic motion?
5) What is the relationship between friction and periodic motion?
6) What is the principle behind the working of a pendulum?
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