A simple pendulum makes 15 oscillations in 30 seconds. What is the time period and frequency of its oscillation?
A. 2 sec, 2 Hz
B. 2 sec, 1 Hz
C. 2 sec, 0.5 Hz
D. 2 sec, 4 Hz
VerifiedHint: Time period is the total time taken by the body to complete 1 oscillation about its mean position. While frequency is defined as the number of oscillations made by the body about its mean position in 1 sec.
\[T = \dfrac{1}{f}\]
Complete answer:
Time period is the total time taken by the body to complete 1 oscillation about its mean position. While frequency is defined as the number of oscillations made by the body about its mean position in 1 sec. There is a mutual connection between time period and frequency which is given as:
\[T = \dfrac{1}{f}\]
According to the question the body makes 15 oscillations in 30 seconds so going by the definition of time period, the time taken to complete 1 oscillation is
\[T = \dfrac{{30}}{{15}}\sec = 2\sec \]
And going by the definition of frequency, one oscillation is completed in
\[f = \dfrac{{15}}{{30}}Hz = 0.5Hz\]
This can also be done by the formula connecting the two parameters
\[f = \dfrac{1}{T} = \dfrac{1}{2}Hz \\
\therefore f = 0.5\,Hz \]
Hence, the time period is 2 seconds and the frequency is 0.5 Hertz.
Therefore, the correct answer is option C.
Note: There is a saying ‘Work Smart not hard’. So, looking at the options given in the question, we note that the time period is the same in all options i.e. 2 sec. Using only the relation T=1/f, we would have got our answer. Apply this method in other similar questions to save time and energy especially in competitive exams.
