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. sig.gif?tid=2N74-08-DD-43-8D37-13518No Attempt No Attempt25% Part (c) Determine the length L in meters of the chandelier. sig.gif?tid=2N74-08-DD-43-8D37-13518No Attempt No Attempt25% Part (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

Answer:

a) 0,1613 Hz

b) 1,01342 rad/sec

c) 9.5422 m

d) $9.4314 m/sec^2$

Explanation:

In the Albert Michelson exhibit at Clark University, we know the period of oscillation of the chandelier is T = 6.2 seconds

The chandelier will be modeled as a simple pendulum

a) Since the frequency is the reciprocal of the period, we have

$f=\frac{1}{T}=\frac{1}{6.2sec}=0,1613 Hz$

b) The angular frequency is computed as

$w=2\pi f=2\pi (0,1613) = 1,01342\ rad/sec$

c) The period of a simple pendulum is given by

$T=2\pi \sqrt{\frac{L}{g}}$

Where L is its length and g is the local acceleration of gravity (assumed 9.8 $m/sec^2$ for this part)

We want to know the length of the pendulum, so we isolate L

$L=\frac{T^2g}{4\pi^2}$

$L=\frac{(6.2)^2(9.8))}{4\pi^2}=9.5422 m$

d) While hanging out in J.J. Thompson’s House O’ Blues, the new period is 6.2+0.11=6.32 sec. Since the chandelier is the very same (same length), we can assume the gravity is slightly different. We use again the formula for T, but now we'll isolate g as follows

$g=\frac{4\pi^2L}{T^2}=\frac{4\pi^2(9.5422m))}{(6.32sec)^2}$

Which results  

$g=9.4314\ m/sec^2$