Why does the period of a pendulum depend on length and free-fall acceleration?

1 Answer
Sunayan S
Mar 7, 2018

Key References:-

  • #k-># angular frequency
  • #a-># accerelation
  • #m->#mass
  • #omega->#angular velocity.

Explanation:

The period (#"T"#) of a pendulum depends upon the length (#"l"#) and gravitational acceleration (#"g"#) because

  • These depends upon the angular velocity (#omega#).

    As a condition for an SHM,

    #F prop -x#
    #=>ma=-kx#
    #=>a=-(k/m)x#
    #=>a=-omega^2x" ; "omega=sqrt(k/m)#

In the given case , #a="g and "x=l" "# i.e ,

We again know that

#"T"=(2pi)/omega#
#=>T=(2pi)/(sqrt(l/g)" "#[ignoring the #-#ve sign as it only indicates the direction of the SHM]

#=>color(red)(ul(bar(|color(green)(T=2pisqrt(l/g))|#

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