Question

A pendulum oscillate 60 times 3 second. Find its Time period and frequency.

Answer 1

$\huge\mathbb{SOLUTION:-}$

$\sf\bullet Number\:of\: oscillation= 60\\ \\ \sf\bullet Time\:taken=3sec$

• So,

$\boxed{\sf{\star{Time\:Period=\dfrac{Time\:taken}{Number\:of\: oscillations}}}}$

$\underline{\sf{\blue{Frequency=\dfrac{1}{T}}}}$

• or

$\boxed{\sf{\bigstar{Frequency=\dfrac{No.\:of\: oscillation}{Time\:taken}}}}$

• First find the Time period

$\sf\implies Time\: Period=\dfrac{\cancel3}{\cancel{15}}\\ \\ \sf\implies Time\: Period=\dfrac{1}{5}\\ \\ \sf\implies Time\: period=0.2second$

Now find the Frequency

$\sf\implies Frequency=\dfrac{No.\:of\: oscillation}{Time\:taken}\\ \\ \sf\implies frequency=\dfrac{60}{3}\\ \\ \sf\implies frequency=\cancel{\dfrac{60}{3}}\\ \\ \sf\implies frequency=20Hz$

$\boxed{\sf{\dag{Time\: period=0.2sec}}}$

$\boxed{\sf{\dag{frequency=20Hz}}}$

Answer 2

Given ,

No. of oscillate(wavelength)=60

Time taken =3 sec

To Find out:

Time period =?

Frequency =?

Formula used:

$\star\mathbf \red{time \: period = : \frac{time \: taken}{no. \: of \:osc. } }$

$\star \mathbf \red{frequency = \frac{no. \: of \: osc.}{time \: period} }$

Solutions:

$\mathbf{time \: period \: = \frac{3}{60} }$

$\mathbf \red{ time \: period = 0.1sec}$

Now,

$\mathbf \red{frequency = \{3} }$

$\mathbf \blue{frequency = 20 Htz}$