The Reflection Of The Definition Of A Simple Pendulum
When a pendulum bob is displaced from its equilibrium position, hanging vertically, …show more content…
This can also be described using frequency per oscillation, which measures how many oscillations it does per second. Frequency is inverse of the period, f = 1/T. Also the period is inverse of the frequency, T = 1/f. We know that the horizontal component of the force is Tsinθ = -ma and the vertical component of the force is Tcosθ = mg. Therefore we can say that:
Tsinθ/Tcosθ= (-ma)/mg tanθ= (-a)/g
In our investigation we are going to keep the angle θ of the pendulum very small therefore we can say that the length L is going to be approximately the same for T. Also tanθ will approximately equal to sinθ. sinθ=(-a)/g x/l= (-a)/g ∴a=(-x)/l g
Using the laws of circular motion we can calculate the time period using the values for a we found above. w=2πf a=-(〖w)〗^2 x
Where w is the angular speed and f is the frequency. Using the equation above for a we can set it equal to the one we found previously to find T using f from angular speed.
(-x)/g=-(〖2πf)〗^2 x g/l=(〖2πf)〗^2 √(g/l)=2πf f=√(g/l)/2πf T=2π√(l/g)
We can also solve for g to find the acceleration due to gravity from our result by rearranging the equation.