A clown is rocking on a rocking chair in the dark. His glowing red nose moves back and forth a distance of 0.42m exactly 30 times a minute in a simple harmonic motion. (a) what is the amplitude of this motion? (b) what is the period of this motion? (c) what is the frequency of this motion?
I don't understand the question
To find the answers, let's break down the information given:
(a) Amplitude is the maximum distance from the equilibrium position. In this case, the distance the clown's nose moves back and forth is the amplitude. We are given that the distance is 0.42 m, so the amplitude is 0.42 m.
(b) The period is the time it takes to complete one full cycle. In this case, we are told that the clown's nose moves back and forth 30 times a minute. To find the period, we need to convert the frequency from minutes to seconds. Since 1 minute is equal to 60 seconds, the clown's nose moves back and forth 30/60 times per second. Therefore, the period is 1/(30/60) = 2 seconds.
(c) Frequency is the number of cycles per unit of time. In this case, we are told that the clown's nose moves back and forth 30 times a minute. To find the frequency, we also need to convert the time from minutes to seconds. So, the frequency is 30/60 = 0.5 cycles per second or Hertz (Hz).
To find the answers, we need to understand the concepts of amplitude, period, and frequency in simple harmonic motion.
(a) Amplitude:
The amplitude is the maximum displacement or distance from the equilibrium position in simple harmonic motion. In this case, the nose moves back and forth a distance of 0.42m. Therefore, the amplitude of this motion is 0.42m.
(b) Period:
The period is the time taken to complete one full cycle of motion. In this case, it is given that the nose moves back and forth exactly 30 times a minute. To find the period, we need to convert the time to seconds since the SI unit of time is seconds.
1 minute = 60 seconds
So, the time taken for 30 cycles would be (30 cycles / 60 seconds) = 0.5 seconds.
Therefore, the period of this motion is 0.5 seconds.
(c) Frequency:
The frequency is the number of cycles or oscillations per unit time. It is the reciprocal of the period. So, to find the frequency, we need to take the reciprocal of the period.
Frequency = 1 / Period
Frequency = 1 / 0.5 seconds
Frequency = 2 Hz
Therefore, the frequency of this motion is 2 Hz.
amplitude=.92m
period=30/60 times/second
f=1/period