91Ó°ÊÓ

When we think about simple harmonic motion, amplitude plays a crucial role. Amplitude is the greatest distance the object moves from its central position, known as the equilibrium position. In this case, the object is initially displaced by 0.120 meters. As it oscillates, it reaches this maximum distance on either side. To find the amplitude, we simply look at this maximum displacement, which remains consistent throughout the motion.
In the given problem, since the object moves from 0.120 meters to the opposite extremity of -0.120 meters, both these values show the amplitude. So, the calculated amplitude is:

• 0.120 meters

The amplitude tells us how far from the starting or central point the motion occurs. This information can be useful in understanding how much energy is stored in the motion, as larger amplitudes usually imply more energy.

The period of oscillation is the time it takes for the object to complete one full cycle of motion. Imagine watching the object start from the extreme of one side, move past its central equilibrium position, reach the extreme of the opposite side, and return back to the starting point.
In this problem, the problem states that it takes 0.800 seconds for the object to move from one extreme to the other and back past the equilibrium. This covers half of an oscillation cycle. Therefore, to complete one full cycle, it would take twice that time:

• Period, \( T = 2 \times 0.800 \text{ s} = 1.600 \text{ s} \)

Knowing the period helps us understand how quick or slow the oscillations are, which directly relates to the energy and force interactions in the system.

Frequency of oscillation is all about how often the object oscillates in one second. It's a measure of how quickly things happen in oscillatory motion. The frequency is the inverse of the period. In simple harmonic motion, the connection between frequency and period is fundamental.
Since the period \( T \) for our system is 1.600 seconds, we can find the frequency \( f \) using this relationship:

• Frequency, \( f = \frac{1}{T} \)
• Substitute \( T = 1.600 \text{ s} \)
• \( f = \frac{1}{1.600 \text{ s}} = 0.625 \text{ Hz} \)

Frequency tells us how many oscillations happen per second. In practical scenarios, a higher frequency implies quicker oscillations, and it can often be a crucial factor in processes where timing and pace are essential.