Question

A pendulum oscillates 40 times in 4 seconds. Find it's time period and frequency.​

Answer 1

Given :-

• A pendulum oscillates 40 times in 4 seconds.

To Find :-

• It's time period and frequency

Solution 1 :-

Frequency of oscillation is defined as the number of oscillation of a vibrating body per second. it is given by

$\boxed{\sf Frequency = \dfrac{Number \: of \: oscillation}{Time}}$

Substituting the values we get,

$:\implies\sf Frequency = \dfrac{\cancel{40}}{\cancel4}$

$:\implies\sf Frequency = 10 \: Hz$

∴ The frequency is 10 Hz.

Solution 2 :-

The time period

The time required to complete one oscillation is known as Time period.

It is given by the inverse of the frequency.

$\boxed{\sf Time \: period = \dfrac{1}{Frequency \: of \: oscillation}}$

Substituting the value we get,

$:\implies\sf Time \: period = \dfrac{1}{10}$

$:\implies\sf Time \: period = 0.1 \: s$

∴ The time period is 0.1 s.

Answer 2

$\huge {\mathtt {\green {\underline {\underline {Given}}}}}$

• A pendulum oscillates 40 times in 4 seconds.

$\huge {\mathtt {\purple {\underline {\underline {To\:Find}}}}}$

• Time period and
• Frequency

$\huge {\mathtt {\red {\underline {\underline {Solution}}}}}$

${\sf Frequency = \dfrac{Number \: of \: oscillation}{Time}}$

Substituting the values we get,

$:\implies\sf Frequency = \dfrac{\cancel{40}}{\cancel4}$

$:\implies\sf Frequency = 10 \: Hz$

${\boxed{\underline{\sf{The \: Frequency \: is \:10Hz}}}}$

${\sf Time \: period = \dfrac{1}{Frequency \: of \: oscillation}}$

Substituting the value we get,

$:\implies\sf Time \: period = \dfrac{1}{10}$

$:\implies\sf Time \: period = 0.1 \: s$

${\boxed{\underline{\sf{The \: time\: period\: is \:0.1 s.}}}}$

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Hope it helps ✔