1. A pendulum has a period of 3 seconds. What's its frequency? 2. A pendulum has a frequency of 0.25 Hz. What's its period? 3. A pendulum makes 10 back and forth swings in 20 seconds. What's its period AND frequency?

(1) 0.333 Hz

(2) 4 sec

(3) 2 sec, 0.5 Hz

Explanation:

(1) We have given time period of pendulum is 3 sec

So T = 3 sec

Frequency will be equal to

(2) Frequency of the pendulum is given f = 0.25 Hz

Time period is equal to

(3) It is given that a pendulum makes 10 back and forth swings in 20 seconds

So time taken to complete 1 back and forth swings =

So time period T = 2 sec

Frequency will be equal to

(1) 0.33 Hz

(2) 4 s

(3) 2 s, 0.5 Hz

Explanation:

The relation between frequency and time period is given as

(1) Given a pendulum has a period, T = 3 s.

So,  

f = 0.333 Hz.

Thus, frequency of pendulum is 0.33 Hz.

(2) Given a pendulum has a frequency, f = 0.25 Hz.

So,

T = 4 s.

Thus , period of pendulum is 4 s.

(3) Frequency is measured in cycles/second.

Given a pendulum makes 10 back and forth swings in 20 seconds.

So,

f = 0.5 Hz

Time period,  

T = 2 s.

Thus, period and frequency of pendulum are 2 s and 0. 5 Hz respectively.