# Math Help - Length of pendulum

1. ## 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

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

solve for $L$ ...

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

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

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

calculate the value of $L$

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

solve for $L$ ...

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

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

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

calculate the value of $L$
How do I find the length using x(t)=10cos(2t)*0.95^t ???

4. 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.

5. 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

6. 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.