Period and frequency question

In summary, the question is about the difference in period and frequency between an adult and a child swinging on identical swings. The answer is that the adult will swing with a much greater frequency than the child. This is because the period of a pendulum is not affected by the mass of the swinging object, but rather the length of the pendulum and the acceleration due to gravity. The equation T=2pi(m/k)^(1/2) is for a spring-and-mass system, not a pendulum, which is why it includes a mass term. The correct equation for the period of a pendulum is T=2pi(sqrt(l/g)).
  • #1
SAT2400
69
0
URGENT//Period and frequency question

Homework Statement


1) An adult and a child are sitting on adjacent identical swings. Once they get moving, the adult, by comparison to the child, will necessarily swing with
a) a much greater period
b) a much greater frequency
c) the same period
d) the same amplitude


Homework Equations


T= 2pi(square root of m/k)


The Attempt at a Solution



THe answer is a B... Can anyone explain why?? I think it's an A b/c as m increases, the T increases??!
 
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  • #2


I recall the following:
For small angles of excursion (i.e. for cases when the pendulum is gently swinging over a few degrees) the period of a pendulum approximates: t = 2*pi*(sqrt(l/g)). There is no term in this equation for mass, which in itself suggests that the size of the swinging mass is not important in determining the period. (l is length of pendulum, g is acceleration due to gravity)
As for the amplitude of the swinging, this has to do with the amount of force used to start the swinging. If the adult is twice the mass of the child, then for the same amplitude of swinging twice as much force (F=m.a) is required.
 
  • #3


Thank you for the reply...

The answer is B. Do you agree with this??

Some of my classmates think it's a C...

Could you please explain again why the answer is a B??

Thank you very much T_T
 
  • #4


well, I'm a bit worried about the relation you have given for the period of the pendulum. Are you quite sure it's a swinging. non-elastic pendulum?

I suggest the following: take a short length of string and try the period of different masses.

You'll find that mass of pendulum makes no observable difference to the period. But there is what looks like a mass term in the relation you have given, and I wonder why. This leads me to worry that I haven't seen the whole picture. I don't want to get this wrong...

I wonder where you got the relation T=2pi(m/k)^(1/2) from?
 
  • #5


SAT2400 said:

Homework Equations


T= 2pi(square root of m/k)

That's the period of a spring-and-mass. Look up the period of a pendulum .
 

What is the difference between period and frequency?

The period of a wave is the time it takes for one full cycle to occur, while frequency is the number of cycles that occur in one second.

How are period and frequency related?

Period and frequency are inversely related. This means that as the period increases, the frequency decreases and vice versa.

What is the unit of measurement for period and frequency?

The unit of measurement for period is seconds (s), while the unit for frequency is hertz (Hz).

How can I calculate period and frequency?

The period can be calculated by dividing the total time by the number of cycles, while frequency can be calculated by dividing the number of cycles by the total time.

Can period and frequency be applied to all types of waves?

Yes, period and frequency can be applied to all types of waves, including sound waves, light waves, and water waves.

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