If ω = 2π/T = 2πf then:

Steps to Solve

1. Understanding Relationships We have the equation for angular frequency given by ( \omega = \frac{2\pi}{T} = 2\pi f ). This implies that angular frequency ( \omega ) is inversely proportional to the time period ( T ) and directly proportional to the frequency ( f ).

2. Rearranging the First Equation Starting from the equation ( \omega = \frac{2\pi}{T} ), we can rearrange it to solve for ( T ): $$ T = \frac{2\pi}{\omega} $$

3. Relating Frequency and Period From the equation ( \omega = 2\pi f ), we can express the frequency ( f ) in terms of angular frequency ( \omega ): $$ f = \frac{\omega}{2\pi} $$

4. Finding the Period in Relation to Frequency Using the relationship between frequency and period, where ( T = \frac{1}{f} ), we substitute ( f ): $$ T = \frac{1}{\frac{\omega}{2\pi}} = \frac{2\pi}{\omega} $$

5. Identifying Correct Options From the rearrangements:

• We see ( T \neq \omega ) and ( T \neq f ).
• The relation ( \omega = T f ) can be derived since ( \omega = 2\pi f ).
• Hence, the options ( \omega T f = 1 ) does not hold true and ( T = 1/f ) is valid.