Skip to main content

Simple Harmonic Motion

SHM is a kind of periodic motion. We can say that all SHM's are periodic but all periodic motion are not SHM. 

Conditions for SHM:

  • The acceleration of the body or the particle should be proportional to the negative of displacement.
  • The total Mechanical Energy of the system remains conserved.
  • There must be a state of stable equilibrium.

Equation of SHM

Consider a particle revolving around a circular path of radius ''a''. with a constant angular velocity ω.
Let at time t=0,

the particle is at the position A then the projection of the particle will be at the point B on the y-axis. So when the particle comes at the top the projection also comes at the top.
Hence we can see that the particle is doing periodic motion but the projection is doing SHM. Hence the time period of the SHM is same as the time period of the circular particle.

The derivation of the actual equation of the SHM is a bit complex and it is difficult for me to show it here so for that you can refer any renowned book like HC Verma for help.

Y=Asin(ωt+Φ)

where Y show the displacement of the particle from its mean position.
A is the amplitude or maximum displacement of the particle from its mean position.
(ωt+Φ) shows the actual phase of the particle and the Φ here shows the initial phase of the particle.

Time period of some important SHM's 

Related image
  • Spring-mass system
The spring-mass system also performs SHM until no external force is applied to it.
Time Period(T)=2π √(m/k)



  • Bob and Pendulum
The simple pendulum also performs SHM
but the angular amplitude should be very small.
T=2π √(l/g)

I hope this gives you a nice idea about SHM. I will soon post a new post on Waves. 

Comments

Post a Comment

Popular posts from this blog

Limitations of Mendeleev's Periodic Table

Mendeleev arranged 63 elements known at that time in the periodic table. According to Mendeleev “the properties of the elements are a periodic function of their atomic masses.” The table consists of eight vertical column called ‘groups’ and horizontal rows called ‘periods’ Limitations of mendeleev’s classification : (i) He could not assign a correct position of hydrogen in his periodic table, as the properties of hydrogen resembles both with alkali metals as well as with halogens. (ii) The isotopes of the same element will be given different position if atomic number is taken as basis, which will disturb the symmetry of the periodic table. (iii) The atomic masses do not increases in a regular manner in going from one elements to the next. So it was not possible to predict how many elements could be discovered between two elements.
42 comments
Go ahead for more »

Statistics Formulas and Important Points

Mean Deviation=Sum of Deviations by Number of observations The Deviation here means the difference of the observations from any of the central tendencies. But mostly we take the Deviation from Mean or Median but not from Mode. Before we see more formulas we should see that the need for Mean Deviation is to get more accurate quantity to relate different quantities. Here are the steps for finding Mean Deviation: (a.) MD for Ungrouped Data We derive the desired Central Tendencies. We find the value of mod(x-a) for all x. We use the formula for calculating MD: (b.) MD for Grouped Data Types of Grouped Data Discrete Frequency Distribution Continuous Frequency Distribution   Discrete Frequency Distribution We find the desired Central Tendency by the formulas of basic Statistics. We find the value of mod(x-a) for all frequency and observations. We find the value of f×mod(x-a) for all frequency and observations. We find MD by this formula: For Central...
6 comments
Go ahead for more »