Question

A swinging pendulum completes 25 oscillations in 8s,
a. what is the time-period?
b. what is the frequency of vibration?

Answer 1

Solution :

⏭ Given:

✏ No.of oscillations = 25

✏ Time interval = 8s

⏭ To Find:

1. Time period
2. Frequency of vibration

⏭ Concept:

✏ Time period is defined as time requires to complete one oscillation.

✏ Frequency is defined as the number of waves that pass a fixed point in unit time or the number of cycles or vibrations undergone during one unit of time by a body in periodic motion.

⏭ Formula:

✏ Formula of time period is given by

$\star \: \underline{ \boxed{ \bold{ \sf{ \pink{Time \: period = \dfrac{Total \: time \: to \: complete \: n \: oscillations}{n}}}}}} \: \star$

✏ Formula of frequency is given by

$\star \: \underline{ \boxed{ \bold{ \sf{ \green{ \large{Frequency = \frac{1}{Time \: period}}}}}}} \: \star$

⏭ Calculation:

• Time period

$\implies \sf \: T = \dfrac{8}{25} \\ \\ \implies \: \boxed{ \sf{ \red{T = 0.32 \: s}}} \: \bigstar$

• Frequency

$\implies \sf \: \nu = \dfrac{1}{0.32} \\ \\ \implies \: \boxed{ \sf{ \orange{ \nu = 3.125 \: {s}^{ - 1}}}} \: \star$