Does mass affect the period of a pendulum attached to an elastic string?

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    Pendulum Period
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The discussion centers on the effect of mass on the period of a pendulum attached to an elastic string. Participants explore whether adding mass to the system changes the pendulum's period, referencing the formula T = 2π√(l/g) for a simple pendulum. It is noted that the period is dependent on the length of the string and gravitational acceleration, not the mass itself. Questions arise regarding the elastic nature of the string and how its extension affects the overall length used in calculations. The conversation emphasizes the need for clarity on the string's properties and the correct application of pendulum equations.
lphalo
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if if we have a string and a object with mass m connected to it , it does extend for 11 cm (string) . if we put another object with the same mass m , what will be the period of that ( of the 2 objects in the string) . please explain does mass affect the period ?
thnx
 
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Hint: Can you derive the formula for the period of a simple pendulum? Draw a free body diagram of a weight on a string not quite in the vertical position. Write the equation of motion. What can you conclude from the equation you derive?
 
LawrenceC said:
Hint: Can you derive the formula for the period of a simple pendulum? Draw a free body diagram of a weight on a string not quite in the vertical position. Write the equation of motion. What can you conclude from the equation you derive?

i cannot derive , cause we didnt learn it , in one conclusion that i made it 'is 2 times more than the first' but i do not have a idea if its true and even if its true is my equation right :S
 
LawrenceC said:
Hint: Can you derive the formula for the period of a simple pendulum? Draw a free body diagram of a weight on a string not quite in the vertical position. Write the equation of motion. What can you conclude from the equation you derive?

wait , even if we didnt learn this part i saw that for a string the T is 2pi square root of l /square root of g , it doesn't affect,, hmm but what must i do to find the period , i only have the increased'' length of 11cm and not the actual length before that
 
Is the string elastic and stretches? I'm not sure I gather that from the problem statement.
 
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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