Question

A pendulum osclllates 50 times in 30 seconds. Find the time period and frequency

Answer 1

t=30s
f=oscillations/time
f=50/30
f=5/3
f=1.67hz

Answer 2

Answer:-

$\red{\bigstar}$ Time Period $\large\leadsto\boxed{\rm\pink{0.6 \: seconds}}$

$\red{\bigstar}$ Frequency $\large\leadsto\boxed{\rm\pink{1.67 \: Hz}}$

• Given:-

Pendulum oscillates 50 times in 30 seconds

• To Find:-

• Time Period
• Frequency

• Solution:-

✴ Frequency:-

We know,

$\pink{\bigstar}$ $\large\underline{\boxed{\orange{F = \dfrac{No. \: of \: oscillations}{Total \: time \: taken}}}}$

• Substituting in the Formula:-

➙ $\sf F = \dfrac{50}{30}$

➙ $\sf F = 1.666666667$

➙ $\bf\red{F = 1.67 \: Hz}$

✴ Time Period:-

We know,

$\pink{\bigstar}$ $\large\underline{\boxed{\orange{T = \dfrac{1}{f}}}}$

where,

• T = time period
• f = frequency

• Substituting in the Formula:-

➙ $\sf T = \dfrac{1}{1.67}$

➙ $\sf T = 0.598802395$

➙ $\bf\red{T = 0.6 \: sec.}$

Therefore, the time period is 0.6 seconds and frequency is 1.67 Hz.