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Harmonic Motions of Similar Models. The unifying power of mathematical methods results to a large extent from the fact that different physical (or other) systems may have the same or very similar models. Illustrate this for the following three systems (a) Pendulum clock. A clock has a 1-meter pendulum. The clock ticks once for each time the pendulum completes a full swing, returning to its original position. How many times a minute does the clock tick

Sagot :

Answer:

tick = 30

Explanation:

The angular velocity in a simple pendulum is

          w² = g / L

the angular velocity is related to the period

          w = 2π/ T

let's substitute

          [tex]\frac{4 \pi }{T^2} = \frac{g}{L}[/tex]

           T = [tex]2 \pi \sqrt{\frac{L}{g} }[/tex]

indicate that the length is m = 1, if we assume that the acceleration of gravity is g = 9.8 m / s²

           T = 2π  [tex]\sqrt{\frac{1}{9.8} }[/tex]

           T = 2.0 s

the clock has a tick each period and since the period is 2.0 s, to complete the minute (60 s) you need

           

           tick = 1 60 / T

           tick = 1 60/2

           tick = 30

The clock ticks 30 times in a minute.

Given that the clock ticks only when the pendulum makes one full swing and complete on cycle and returns to its original position. To calculate how many times the clock ticks we need to calculate the time period of the pendulum swing.

For a pendulum, the time period (T) is given by:

[tex]T=2\pi \sqrt\frac{L}{g}[/tex]

where g is the acceleration due to gravity = 9.8[tex]m/s^{2}[/tex],

and L is the length of the pendulum = 1m (given)

[tex]T=2*3.14 \sqrt\frac{1}{9.8}[/tex]

[tex]T=2s[/tex]

So, the pendulum takes 2 seconds to complete a cycle.

2s = 1 tick

60 second = 60/2 = 30 ticks

It will tick 30 times in a minute.

Learn more about pendulum:

https://brainly.com/question/20070798

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