Question

State the way through which we can prepare a pendulum by our own. Explain with reference to a pendulum time period , frequency, amplitude ​

Answer 1

Answer:

A simple pendulum has a heavy point mass (known as bob) suspended from a rigid support by a massless and inextensible string. When the bob from its mean position is pulled to one side and then released, the pendulum is set to motion and the bob moves alternately on either side of its mean position.

These are important terms pertaining to simple pendulum:

1. Oscillation: One complete to and fro motion of the pendulum is called one oscillation

2. Time period: This is the time taken to complete one oscillation.

3. Frequency of oscillation: It is the number of oscillations made in one second.

Explanation:

Answer 2

Answer:

Basic construction of a pendulum:

• Place a 12-inch ruler on the end of a table or desk. The end of the ruler should stick out 4 inches from the end of the table.
• Place a heavy book on top of the ruler to hold it in place. Mark 3 (1/2)-foot piece of string at 19 (1/2) inches, 27 inches and 35 (1/2) inches with a marker. Please tie the string to the end of ruler.

• Tie the loose end of the string to a 3 (1/2) ounces weight. You can use anything for weight of  3 1/2 ounces until it can be tied to the string which is generally called bob.

• Make a note of the length of the string from the weight to the knot at the ruler. Pull the bob to the side and leave it and allow it to make 10 full swings.

For simple pendulum:-

$Ft=-mgsin\theta=md^2sdt^2$

For small displacement, where sinθ=0 and along the arc is the motion of the bob, then

s = Lθ

Therefore, $\frac{d^2\theta} {dt^2}=-\frac{g}{L}sin\theta=-\frac{g}{L}\theta$

$\frac{d^2\theta} {dt^2}+\frac{g}{L} \theta=0$

$\frac{d^2\theta} {dt^2}+\omega^2_n \theta=0$

where $\omega_n$ is the angular frequency of oscillations,  $\omega_n=\sqrt{\frac{g}{L} }$

$\omega =2\pi f$

Time period is defines as the time taken by pendulum to complete its one oscillation.

The period of motion is $T= \frac{2\pi }{\omega_n}=2\pi \sqrt{\frac{L}{g} }$

Frequency (f) is defined as the the number of oscillations made by pendulum in one second.

$f =\frac{1}{T}$

Amplitude is defined as the maximum displacement from its mean position.

$f(x)= A sin(wt)$

where A is the amplitude and x is the displacement by pendulum .

The time period of oscillations of a simple pendulum is independent of the amplitude of oscillations. Therefore, even if a pendulum is made to swing in a bigger amplitude its the time period, angular frequency and  frequency remains same.

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