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.  

scientific laws are the result of testing theories and proving them to be facts.

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .