A simple harmonic oscillator takes 13.0 s to undergo seven complete vibrations.
(a) Find the period of its motion.
(b) Find the frequency in hertz.
(c) Find the angular frequency in radians per second.
(a) 13/7 s
(b) 7/13 hz
(c) 7π / 13 rad/s
ω = 2πf
To find the period of motion, we use the equation:
T = t/N
where T is the period, t is the time taken, and N is the number of complete vibrations.
(a) To find the period of motion:
T = 13.0 s / 7
Calculating:
T = 1.857 s
Therefore, the period of the motion is 1.857 seconds.
(b) To find the frequency in hertz:
f = 1 / T
Calculating:
f = 1 / 1.857
Therefore, the frequency is approximately 0.538 Hz.
(c) To find the angular frequency in radians per second:
ω = 2π / T
Calculating:
ω = 2π / 1.857
Therefore, the angular frequency is approximately 3.386 rad/s.