# Length of pendulum

• Jun 12th 2009, 03:07 PM
yoman360
Length of pendulum
the motion of a pendulum can be modelled by the function x(t)=10cos(2t)*0.95^t, where x is the horizontal displacement from the rest position, in centimetres, as a function of time, t, in seconds
Determine the length of the pendulum.

answer is 245 cm in the book, i want to know the steps, thanks
• Jun 12th 2009, 05:01 PM
skeeter
Quote:

Originally Posted by yoman360
the motion of a pendulum can be modelled by the function x(t)=10cos(2t)*0.95^t, where x is the horizontal displacement from the rest position, in centimetres, as a function of time, t, in seconds
Determine the length of the pendulum.

answer is 245 cm in the book, i want to know the steps, thanks

period of a pendulum, $\displaystyle T = 2\pi\sqrt{\frac{L}{g}}$

solve for $\displaystyle L$ ...

$\displaystyle L = \frac{gT^2}{4\pi^2}$

$\displaystyle T = \frac{2\pi}{2}= \pi$

$\displaystyle g = 980 \, cm/s^2$

calculate the value of $\displaystyle L$
• Jun 12th 2009, 05:36 PM
yoman360
Quote:

Originally Posted by skeeter
period of a pendulum, $\displaystyle T = 2\pi\sqrt{\frac{L}{g}}$

solve for $\displaystyle L$ ...

$\displaystyle L = \frac{gT^2}{4\pi^2}$

$\displaystyle T = \frac{2\pi}{2}= \pi$

$\displaystyle g = 980 \, cm/s^2$

calculate the value of $\displaystyle L$

How do I find the length using x(t)=10cos(2t)*0.95^t ???
• Jun 12th 2009, 06:17 PM
skeeter
Quote:

Originally Posted by yoman360
How do I find the length using x(t)=10cos(2t)*0.95^t ???

the only piece of information you can determine from the given position equation is the period of oscillation.
• Jun 12th 2009, 06:20 PM
yoman360
Quote:

Originally Posted by skeeter
the only piece of information you can determine from the given position equation is the period of oscillation.

so basically x(t)=10cos(2t)*0.95^t is pointless info
• Jun 13th 2009, 04:03 AM
skeeter
Quote:

Originally Posted by yoman360
so basically x(t)=10cos(2t)*0.95^t is pointless info

not pointless ... but you cannot determine the length of the pendulum without the necessary equations of simple harmonic motion from physics.