User:Jyothsna sai/sandbox

SIMPLE HARMONIC MOTION:
It is a special type of periodic motion in which force is always

1.directed towards its mean position.

2.It is function of displacement. where displacement is function of time. F=-Kx. where x is function of time .ie x=A$$\cos(Wt+angle)$$

There are so many systems in the nature exhibits SHM from macroscopic world to microscopic world.

For example : molecule exhibits SHM,spring system exhibits SHM, Simple pendulum exhibits SHM.

Intresting parameter in the SHM is  time period.

TIME PERIOD
It is small time interval in which motion repeats.

COMPARISION OF TIME PERIOD BETWEEN SPRING SYSTEM AND SIMPLE PENDULUM
LET US COMPARE THE TIME PERIOD OF SPRING SYSTEM AND SIMPLE PENDULUM

{| class="wikitable" !

SPRING SYSTEM
!SIMPLE PENDULUM
 * Mass-Spring-Damper.pngTIME PERIOD =2$$\Pi$$$$\surd(m/K)$$
 * Mass-Spring-Damper.pngTIME PERIOD =2$$\Pi$$$$\surd(m/K)$$

1.Time period always depends on mass the reason behind this is spring force doesnt know how much mass you are attaching to it,only displacement does matter to the spring force ie '' F=-Kx. ''

For a certain displacement force is always constant and it is independent of mass when you increase mass same force acts and acceleration decreases so velocity decreases that is why time period increases.

2.The other factor on which time period depends on is spring constant K,for stiff springs K is more so time period will be less.

3.If you take spring system to the space shuttle where g=0 and if you displace mass and release it will execute same oscillations with same time period as if in earth ie, SHM in spring system doesnt depend on g.

Under freefall wrist watch gives same time because it works under action of spring it doesnt depend on g.
 * Pendulum.jpgTIME PERIOD =2$$\Pi\surd(l/g)$$

1.Time period doesnt depends on mass at all the reason behind this is the only component which is responsible for oscillations in this situation is Tsin(A), when you increase mass T increases so force ie Tsin(A) is increasing with mass.

so it is compensating velocity and time period everywhere so time period is independent of mass

2.Time period depends on length when you increase length time period increases,when you decrease length time period decreases.

3.One more intresting factor is if you take simple pendulum to the space shuttle where g=0 because spce shuttle will be under free fall,then time period becomes infinity.

That means pendulum never changes its position at all ie, if you give small angular displacement to pendulum it stays there itself.

You can never find time period and mass of simple pendulum in the space shuttle.
 * }