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There are 2 oscillating pendulums:
pendulum A oscillates - 12 times in 10 secs
pendulum B oscillates - 8 times in 3 secs
Q1. Find out which pendulum has more frequency and by how much?
Q2. Find out which pendulum has more time period and by how much?
Given
In pendulum A
Oscillations - 12 times,
Time taken - 10 secs
To find, frequency and time-period
We know that,
$Frequency (f)=\frac{1}{time(t)}=\frac{no.of cycles/oscillations}{time}$
$f=\frac{12}{10}=1.2Hz$
$f=1.2Hz$
Now, the formula for time-period
$T=\frac{1}{frequency(f)}$
$T=\frac{1}{1.2}=0.83sec$
$T=0.83sec$
In pendulum B
Oscillations - 8 times
Time taken - 3 secs
We know that,
$Frequency (f)=\frac{1}{time(t)}=\frac{no.of cycles/oscillations}{time}$
$f=\frac{8}{3}=2.66Hz$
$f=2.66Hz$
Now, the formula for time-period
$T=\frac{1}{frequency(f)}$
$T=\frac{1}{2.66}=0.37sec$
$T=0.37sec$
Answer to the 1st question
Frequency of pendulum A = 1.2Hz
Frequency of pendulum B = 2.66Hz
Hence, pendulum B has more frequency than A, by 1.46Hz. (2.66 - 1.2 = 1.46)
Answer to the 2nd question
Time-period of pendulum A = 0.83sec
Time-period of pendulum B = 0.37sec
Hence, pendulum A has more time-period than B, by 0.46sec. (0.83 - 0.37 = 0.46)