Question

if a pendulum oscillates 360 times in 3 minutes what is it's time period​

Answer 1

• 3minutes=3(60)=180s
• Oscillations=360

$\\ \sf\longmapsto Time\:Period=\dfrac{180}{360}$

$\\ \sf\longmapsto Time\:Period=0.5s$

Answer 2

Answer:

${ \rm{T = \frac{1}{f} }}$

• T is the period ( time for one oscillation )

• f is the frequency. But :

${ \boxed{ \tt{f = \frac{n}{t} }}}$

• n is the number of oscillations.

• t is the time taken at given number of oscillations.

→ Therefore:

${ \rm{T = \frac{1}{( \frac{n}{t}) } }} \\ \\ { \rm{T = \frac{t}{n} }}$

• substitute:

${ \rm{T = \frac{3 \times 60}{360} }} \\ \\ { \rm{T = 0.5 \: seconds}}$

Period is 0.5 seconds