Question

While visiting the Albert Michelson exhibit at Clark University, you notice that a chandelier (which looks remarkably like a simple pendulum) swings back and forth in the breeze once every

T = 6.2 seconds.Randomized VariablesT = 6.2 seconds(a) Calculate the frequency of oscillation (in Hertz) of the chandelier.(b) Calculate the angular frequency ω of the chandelier in radians/second.
(c) Determine the length L in meters of the chandelier. sig.gif?
(d) That evening, while hanging out in J.J. Thompson’s House O’ Blues, you notice that (coincidentally) there is a chandelier identical in every way to the one at the Michelson exhibit except this one swings back and forth 0.11 seconds slower, so the period is T + 0.11 seconds. Determine the acceleration due to gravity in m/s2 at the club.

Answer 1

a)
`F=0.16Hz`

b)
`\omega=1rad/s`

c)
`L=9.54m`

d)
`g=9.46m/s^2`

Explanation:

From the question we are told that:

Time
`T =6.2`

a)

Generally the equation for Frequency F is mathematically given by:

`F=(1)/(T)`

`F=(1)/(6.2)`

`F=0.16Hz`

b)

Generally the equation for Frequency F is mathematically given by:

`\omega=2\pi f`

`\omega=2*314* 0.16`

`\omega=1rad/s`

c)

Generally the equation for Length of Chandelier L is mathematically given by:

Since

`T=2*3.142\sqrt{(L)/(g)}`

Therefore

`L=(gT^2)/(4 \pi^2)`

`L=(9.8*(6.2)^2)/(4 \pi^2)`

`L=9.54m`

d)

Since

Michelson exhibit except this one swings back and forth 0.11 seconds slower

Therefore

`T'=T+0.11`

`T'=6.31`

Generally the equation for acceleration due to gravity g is mathematically given by:

`g = (4\pi ^2L)/(( T'))^2`

`g = (4\pi ^2L\*9.54)/(( 6.31 s ))^2`

`g=9.46m/s^2`