A mass on a spring bobs up and down over a distance of 30cm from the top to the bottom of its path twice each second. What are its period and amplitude?
twice each second, then f=2hz. period=1/f
amplitude? 15 cm, of course.
To find the period and amplitude of the mass on a spring, we need to understand the terms and equations associated with simple harmonic motion.
First, let's define the terms:
- Period (T): The time taken for one complete cycle of motion.
- Amplitude (A): The maximum displacement of the mass from its equilibrium position (midpoint).
In this case, we're given that the mass completes two cycles each second and covers a distance of 30cm from top to bottom.
To find the period (T), we can use the formula:
T = 1 / f
where f is the frequency, which is the number of cycles per second. In this case, the frequency is 2 cycles/second.
So, T = 1 / 2 = 0.5 seconds.
To find the amplitude (A), we can use the given information that the mass covers a distance of 30cm from top to bottom. The amplitude is half of this distance because it measures the maximum displacement from the equilibrium position.
So, the amplitude (A) = 30cm / 2 = 15cm.
Therefore, the period is 0.5 seconds and the amplitude is 15cm.