1. ## simple pendulum

What is the frequency of the simple pendulum if its in the lift which is accelerating upwards at 2.00 m/s^2 . Given that the length of pendulum is 0.248 m .

I am not sure what 's the acceleration of gravity ..

Thanks .

2. Hello thereddevils
Originally Posted by thereddevils
What is the frequency of the simple pendulum if its in the lift which is accelerating upwards at 2.00 m/s^2 . Given that the length of pendulum is 0.248 m .

I am not sure what 's the acceleration of gravity ..

Thanks .
The period of a simple pendulum is given by

$\displaystyle T = 2\pi\sqrt{\frac{l}{g}}$

where $\displaystyle l$ is the length of the pendulum, and $\displaystyle g$ is the acceleration due to gravity.

If the lift is accelerating upwards at $\displaystyle 2\text{ ms}^{-2}$, then $\displaystyle g$ is effectively $\displaystyle 9.81+2 =11.81\text{ ms}^{-2}$. So with $\displaystyle l = 0.248$:

$\displaystyle T = 2\pi\sqrt{\frac{0.248}{11.81}}=0.9105$ sec

So the frequency $\displaystyle = \frac{1}{T}=1.098$ Hz

Hello thereddevilsThe period of a simple pendulum is given by

$\displaystyle T = 2\pi\sqrt{\frac{l}{g}}$

where $\displaystyle l$ is the length of the pendulum, and $\displaystyle g$ is the acceleration due to gravity.

If the lift is accelerating upwards at $\displaystyle 2\text{ ms}^{-2}$, then $\displaystyle g$ is effectively $\displaystyle 9.81+2 =11.81\text{ ms}^{-2}$. So with $\displaystyle l = 0.248$:

$\displaystyle T = 2\pi\sqrt{\frac{0.248}{11.81}}=0.9105$ sec

So the frequency $\displaystyle = \frac{1}{T}=1.098$ Hz

Thanks Grandad . But i do not understand why is the accleration 9.81 +2

If the lift is accelerating upwards , but the accleration due to gravity is accelerating downwards ..

4. Hello thereddevils
Originally Posted by thereddevils
Thanks Grandad . But i do not understand why is the accleration 9.81 +2

If the lift is accelerating upwards , but the accleration due to gravity is accelerating downwards ..
The technical answer is that you need to find the difference between the vectors representing the two accelerations. So if we take the direction vertically downwards as positive, then the acceleration of the lift is $\displaystyle -2 \text{ ms}^{-2}$, and $\displaystyle g = +9.81$. So the difference is $\displaystyle 9.81-(-2) = 11.81$.

The more intuitive (and simpler) answer is to ask yourself: do you feel heavier or lighter when a lift is accelerating upwards? The answer, of course, is heavier. So the acceleration of the lift is added to the acceleration due to gravity.