Calculating Pendulum Angle and Amplitude: Homework Question and Equations

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To calculate the angular frequency of a pendulum, the relationship between angular frequency and the length of the pendulum is essential, expressed as ω = √(g/L). The period of the pendulum is identified as 6 seconds, leading to the calculation of angular frequency using the formula. The amplitude of the pendulum's motion is noted to be 1 degree. Understanding the distinction between angular frequency and frequency in Hertz is crucial for accurate calculations. Proper manipulation of the equations will allow for the determination of the pendulum's length and further insights into its motion.
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Homework Statement


a)The angle that the string of a long pendulum makes with the vertical is shown as a function of time. What is the angular frequency of the pendulum?
b)What is the amplitude of the pendulum's motion, in meters?

Homework Equations


Angular frequency=sqrt(g/L)

The Attempt at a Solution


im trying to find the length of the pendulum from the graph provided but I am not sure how to do that..
By looking at the graph i think the period is 6 seconds,and the amplitude is 1deg.. but I am not sure how to proceed from here. Any advice would be helpful, Thanks!
 

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Do you know the definiton of angular frequency? Do you know how frequency is related to the period? Do you know how to manipulate the frequency expression you gave to solve for L?
 
Yes, Dr. D is correct up there. Think what the definition of angular frequency is Warning: angular frequency is a bit different from frequency in Hertz you get from graphs as the number of full wavelengths per second.

You already know the relationship between angular frequency and length of the string. (## \omega = \sqrt{\frac{g}{l}} ##)

Now you only have to determine angular frequency from the period that you determined from the graph. Good luck! ^^
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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